(For a video version of this frequently asked question and answer, click this link.)
When you render and export a movie, the default ouptut settings are for files that are not intended for playback. The default on Mac OS is for a QuickTime movie with lossless Animation compression. The default on Windows is for an AVI movie with no compression. An uncompressed or losslessly compressed movie is huge and is not intended for playback; it's intended as an intermediate file for further post-production work. These huge files can't be read from disk fast enough to be played in real time by some computers. For smooth playback on your computer, you need to compress the file. See this page: "Encoding and compression options for movies"
Movies are compressed differently depending on how they are to be used. When they are intended as intermediate files (i.e., as input into another piece of post-production software), they are compressed very little. That is the default from After Effects because After Effects is primarily meant as a compositing, motion graphics, and visual effects tool, and it feeds into other tools, like non-linear editors. If, on the other hand, the movie is intended to be played back from a DVD or distributed over the Web, then the movie is compressed a lot---and in one of many, many specific ways.
The upshot is that you really need to begin by knowing what it is that you want to do with the movie. And then you need to learn about what output options are best for that purpose.
There's a good article from Aharon Rabinowitz linked to from this page that talks about how you need to be thinking about the details of output from the very beginning of a project.
For information about choosing output settings, see this page: "FAQ: What is the best output format for rendering and exporting from After Effects?"