To explain it a bit better, YouTube requires flash to play videos. BlackBerrys don't have flash installed on them. So you need to go to the mobile site link above to access the videos in a different format.
The trade off is the quality is worse and larger videos constantly buffer if your data connection is poor.
To make life easier I recommend downloading the app called Player For YouTube onto your phone, basically gives you a nice interface for searching and viewing apps, also appears to be more stable then other YouTube BlackBerry apps, you can download it from the CrackBerry app store.