Three Dimensional Thinking
The biggest distinction between compressing individual images and a series of moving images is the introduction of a third dimension into the equation. Not only do pixels have similarities to those above and below them, but they can also be compared to pixels that occupy the same or adjoining space in preceding and following frames. In other words pixels close in time.
GOPA Group of Pictures (GOP) is a group of sequential video frames, at least some of which rely on others in the group to be a complete picture. Each GOP starts with a complete image that can be drawn without decoding any other frame. To save space, any information that doesn't change in the next frame can be skipped, and only the changes recorded for the second frame in the GOP. The more a particular frame depends on the contents of other frames, the more potential for inaccurate data there is, but the more compression is achieved as well.
Open GOPsGOPs may be completely self contained, and in some cases may have to be. They can also contain frames that require information from adjacent GOPs. These GOPs are considered opened. Closed, or self contained, GOPs are required by DVD-Video specs for multiple angles or seamless branching (ILVU).
Bidirectional FramesSome comnpression formats allow frames to be built from frames both before and afterward. These bidirectional frames have the advantage of more compression, because so much information comes from other frames, without the errors caused by relying on only one frame. By using combinations of frames that only use information from one other frame but take more space with those that rely more on other frames but are more compressed, a compromise between size and accuracy is achieved that may allow us to use fewer full frames, also known as Key frames.
DrawbacksWhile using a GOP structure will increase compression, it will also cause problems editing later on. If you want to cut a frame out of the middle of a GOP, frames on either side would be affected unless you cut on a key frame of a file with closed GOPs. This is why formats like the various DV variants, which are intended for editing, don't use GOP compression.
MPEG GOP Structure
Since it's so common, it's worth mentioning that MPEG-1 and MPEG-2 refer to key frames as I (Index) frames, frames that rely on one other frame as P (Predictive), and those that rely on frames before and after as B (Bidirectional).