The PS3 can output video in 1080p. The system has a HDMI port that can be connected to a HDTV where you can use the system in 1080p.
The Playstation 3 has support for 1080p, but this does not mean that you will actually be able to play every game in 1080p. The maximum resolution of each game should be printed on the back of each game box. The resolution of the game depends on the developer and what they decide the best resolution is for their game. This is not a decision that Sony make.
If a game is being displayed in 720p and you have a TV that supports 1080p then it is likely due to the game not supporting 1080p.
Make sure you are using the correct cables. The standard red, white and yellow cables that come with the Playstation 3 console do not allow you to output in 1080p. You must get HD cables and change the video output settings.