In order for the audience watching a movie to understand the relationship of characters and significant things within a scene the movie needs to be filmed from a consistent point of view. The 180 rule helps the director preserve that consistency in the minds of the audience. If you were to draw an imaginary line through the film set then all filming must be done from one side of that line, or axis. That, in a nutshell, is the 180 degree rule.
When the audience is seeing a scene of a guy on the left talking to a lady on the right they might be confused if the scene is filmed so the close-ups of both the man and woman seem to be looking in the same direction. If at any time the camera is moved to the reverse side of the axis for one or more shots in a scene the audience will probably be confused and imagine the characters suddenly turned around or jumped to a different place in the scene.
Action and particularly chase sequence scenes particularly need to have the 180 degrees rule followed. Moving from one side of the axis to the other creates an illusion in the minds of the audience that the chase has abruptly changed direction.
When the camera moves across the axis it is referred to as jumping the line or crossing the line. In reality such a change in perspective at some point in a chase sequence would only be fitting in a comedy.
When a scene is being filmed it is usual to do different shots of the characters performing the scene all the way from a wide version that includes everything down to close-ups of single actors. This procedure is known as coverage. Retaining the 180 degree rule is very important when shooting coverage so the editor can put the elements together in a way that makes sense.
Creatively Breaking the 180 degrees rule
Some directors may certainly break the 180 degree rule for a special reason such as to produce disorientation in the audience's mind. You may see this during battle sequences or a dance number. If the action takes the participants round a turn after that it can seem logical to the audience that action is moving in a another direction.
If actors are moving about during the action of a scene much attention needs to be used to maintain the apparent physical correlation of the actors to each other and to the set elements. If the scene is done as all close-ups it will be extremely confusing as to what is going on. An incidental wide, establishing shot can remove the misunderstanding.