Why are the files 10 times bigger after I import my AVCHD into iMovie?

The camera stores the movie in a very compressed codec called AVCHD. When you import to iMovie, it is converted to the Apple Intermediate Codec for editing.

AVCHD is a "group of pictures" compression scheme, which achieves compression by starting with one full frame, and then for the next 24 or so frames, it uses partial frames that attempt to capture what has changed since the full frame. These partial frames will have information like direction of motion, and what has changed from the previous frame.

To give an example, let's say you have a video clip of a duck flying across the sky. The i-frame is a complete "photo" of the scene. It is compressed, much like a JPEG photo is compressed, but it stands alone. The next few frames will have heavily compressed information like "the background is moving left to right at this rate", "the duck is flying right to left", "the duck's wings are going up and down", and everything else stays the same. Then in 24 frames, you do it again.

Apple Intermediate Codec is still somewhat compressed, but each frame stands on its own. It is not dependent on the other frames around it.

This is much better for editing, because if you edit out the full i-frame in a group of pictures, you make the next 24 frames worthless. You can overcome this by converting to full frames as you are editing, but this takes a much more powerful processor and more memory. So the standard practice is to convert everything to full frames on import.

This means that Apple Intermediate Codec can be up to 10 times larger than the file on your camera. (It is not 24 times larger, because the partial frames in GOP compression still take up some room.)

After you have edited the movie, you will use the Share menu to render the movie in the formats and sizes you need. Usually, you will share your movie in the h.264 codec. H.264 is similar to AVCHD, in that it uses GOP compression, so your final movie will be a reasonable size.

By the way, if you had FInal Cut Pro X, your AVCHD would be converted to ProRes 422 (rather than Apple Intermediate Codec) on import, and it would be more than 10x larger. (Technically, Final Cut Pro X can edit AVCHD natively, but in practice, pros will always convert to ProRes 422 because good editing performance is much more important to them than saving space.)

If you import the DV codec from tape, the file sizes are large, but they do not get 10x larger, because DV is already a codec that is all i-frames.

Most people who make a lot of movies will acquire one or more large external drives.