You can export match highlights from your FM games onto your hard drive to watch and do whatever you want with them, the method is the same as uploading to YouTube, the only difference is on the "upload highlights" screen you select export highlight as movie instead of "upload".
Highlights uploaded to YouTube are also stored on your PC if you have "save uploaded videos" ticked in preferences. The location they are stored to is as follows.
"user name"\Documents\Sports Interactive\Football Manager 2012\uploads
Highlights uploaded to YouTube are also stored on your PC if you have "save uploaded videos" ticked in preferences. The location they are stored to is as follows.
"user name"\Documents\Sports Interactive\Football Manager 2012\uploads