Okay, first a simple explanation: if you have two characters talking, draw an imaginary line between them. Now the rule states that you need to keep the camera on one side of that line and never cross over to the other side.

You can put the camera anywhere you want as long as you don't cross the line to the other side of the two characters. This way, no matter what shots you have, you can cut them together in any order and the green character will always stay on the right side of the frame and the blue character will always stay on the left.

If you break this rule and shoot one shot from the other side of the line, the characters will be flopped: the blue guy is now on the right and the green guy is on the left.

This can confuse the audience because, for example, if the characters look similar, they may start to get the two people mixed up. Or they may think that the characters switched places between cuts, or they may think it's a time jump to a different location at a later time or something. It can cause unnecessary confusion in the audience's mind, and we always want to avoid that.
The problem becomes even more apparent when you're doing a scene where people are in action. For example, when a character is running, you want to consider the path they're traveling along as the line that you don't want to cross. Obviously, if you shoot from the other side the line, the character will look like he's going the opposite direction.

If you start to cut these two different shots together you will create a lot of confusion: did the character turn around and start running back the other way? Or is it two characters running towards each other and they're going to collide?
That's why you'll notice that - especially in animated movies - a destination is always kept to one side of the screen or the other and the character is always traveling that way. A good example is in Disney's "Bolt" - Bolt is traveling from New York to Los Angeles and he is always traveling towards screen left. All of us Americans grew up looking at maps of the US with NY on the right hand side and LA on the left so this inherently makes sense to us and it helps keep us clear that he's always traveling towards his goal and not suddenly turning around and heading back towards the East Coast.
So anyway there you go. Probably obvious stuff for everybody...
...but I bring it up because sometimes there are good reasons to break the 180 rule. For a complete discussion of continuity and how to maintain it or break it effectively, I recommend "The Five C's of Cinematography" or "Film Directing: Shot By Shot".
Here's an online clip from the second "Pirates of the Caribbean" movie which has two good examples of breaking the 180 rule. Mild spoilers ahead, I guess...
The first one is when this giant wheel breaks free from it's mounting and goes rolling down a hill. Now as far as the path of action on something like this, it would have to be assumed to be the path that the wheel is traveling. So if you take a shot from one side and then cut it against a shot from the other side, it would look like the wheel was rolling from left to right and then from right to left - two different directions. Right?
At 3:22, you'll notice that there is first a shot from one side of the wheel of the wheel breaking free and starting to roll from the left to the right

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And then, two shots later there's a shot from the other side, of the wheel starting to roll from screen right to screen left

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So clearly these shots break our 180 degree rule. The wheel appears to be going one direction, and then the other. But I like the use of both angles here and I think it works just fine. It clearly shows that the wheel has broken loose on both sides and is now rolling free. Also having two different shots of it starting to roll allows the filmmaker to extend that moment of breaking free for greater emphasis. Also cutting from one angle to another that are opposites like that creates contrast and makes for an exciting and dynamic cut.
There's no possibility for confusion here, because we know there is only one giant wheel in the story at this point, and it couldn't possibly be two different wheels breaking free and rolling towards each other. So I think the "breaking" of the 180 rule here is totally fine. There's really not much risk of the viewer being confused by these cuts.
The other breaking of the 180 rule here happens in the same clip around 4:15. I think that the filmmakers made another smart choice to break the rule here.
Here are the shots, in order:








And here is a diagram showing where the camera is for each shot.

So the "line of Action" is the red line between E (for Elizabeth Swann) and P and R (Pintel and Rigetti, the pirates, and yes, I'm a nerd for knowing their names). Now when the wheel enters, most people that I've worked with would play it safe and say that you should just stay where the camera is in set up (1), that is, just have our foreground characters stop and watch as the wheel rolls through the scene, and then have them go back to their fight with each other all in one continuous shot in setup (1).
But I don't think that's nearly as interesting or entertaining as cutting around to see their faces and register their shock as they take in this unusual sight. So I think the cut around to the other side is warranted and justifiable and adds to the scene. Also the addition of cuts breaks the action into a longer, more extended beat which lasts longer and "milks" the funny moment better than if it just rolled through the one shot.
One smart thing that makes the jump around to the other side work pretty well is that when the camera goes around we only see closeups of the character's faces. That's good because if we saw all three of them in one shot it would throw us off because they would be switching sides of the screen with each other.
But here's where I would have done it a little differently: I would have eliminated shot (5) and rearranged shots (3) and (4).
Here's why: in the first shot, which is (1) and (2), you're back behind them as the wheel, chased by Jack, starts to roll into the background of the scene. Then you jump to shot (4) of Jack running (instead of 3).
This might be better progression because you're cutting closer to the action of the wheel and Jack, and it might feel like a more natural cut to go to Jack running than going to Elizabeth's face. Jack is running the right way, so you haven't really "crossed the line" yet, but by virtue of the camera jumping closer to the action, then if you cut right to (3) and (6) it feels like the camera has first jumped closer to Jack, and then swung around to look at Elizabeth and then the pirates, instead of going back and forth across the line, which is what it feels like in the finished film. So here's what it would look like:







My version has the disadvantage of cutting from Elizabeth to the pirates and back to Elizabeth, which some might say feels weird to see Elizabeth twice in shots so close together, but I don't think that would bother me in actual practice. If it were possible I would probably combine both of Elizabeth's close-ups into one shot (the latter one) for simplicity and to keep it from getting too "cutty". Obviously Gore Verbinski is an awesome director and I'm not saying my version is "better" at all, it's just my own personal preference, based on what I've done before and what I think works better from my own experience and taste. If nothing else hopefully you'll get something out of seeing the two contrasting versions and deciding for yourself what works and what doesn't or you. Run your eyes across the film version and then my version and see what feels better to you. There are many other possibilities for schot order and I'm sure many of them would work great too.
Okay, is everyone confused now? Probably! Sorry. I tried to be clear but....yeech. It's a hard topic to write about and not the most interesting one, I admit! If you're confused leave a comment and I'll try to clarify for you.
There's nothing wrong with my Disney colleague's tendency to keep the screen direction consistent and not to want to experiment with it too much. It's totally understandable - unlike a live-action set, we can't make a physical line on the floor and keep our camera on one physical side of it. Our "lines of action" exist in our minds only, and we don't have physical actors to point the camera at either! Our "actors" exist in the theoretical world and so a lot of care must be taken to make them consistent from scene to scene and artist to artist. All of our shots pass through many departments and the easiest way to organize screen direction simply and consistently to minimize confusion. I just sometimes wish we could take a look at this rule and ask ourselves if we might gain something by setting it aside from time to time. I always want our animated movies to have as sophisticated a visual language as our live-action counterparts.
Okay, so what's the point of all this?
I guess I would say that this nicely fits within my (constantly repeated) philosophy that you should get to know the rules (whether it's filmmaking or drawing). Then as you gain experience and knowledge, you can choose to break the rules, using your experience as a guide to tell you when it's worth it to break the rules - what are you gaining, and what are you losing by breaking this rule or that rule? Too many times people don't have the patience to learn the rules (or principles or guidelines, if you prefer those terms) and they end up breaking all of them all the time, either out of ignorance that the rules exist or a desire to be rebellious for the sheer sake of being rebellious. Our limitations exist for a reason, they are our framework and guide, and if you don't know the rules, then I would say how can you know if you are breaking them?













