I recently received a few .mts files from a friend. These files are AVCHD high-definition video files from consumer-grade HD video cameras, and they've traditionally been a pain to work with.
If you have the files on your camcorder or an SD card from your camcorder, you can just open up iMovie '08 or iMovie '09 and click 'import from camera.' It'll take forever to transcode the files into something iMovie can use, but it will work. If, however, you're like me and you just have the files (no camcorder), you'll need to transcode the files before you can edit them or compress them further.
The easiest way to do this, in my experience, is to use Handbrake, the best/simplest transcoding software you can get on the Mac... and it's free! Don't pay any money for fancy GUI wrappers like the ones you'll find on mtsconverter.com, applemacvideo.com, mtsconvertermac.biz, etc... these are all ripoffs of ffmpeg, a free and open source video transcoding library.