The Playstation 3 supports a maximum resolution of 1080p, but the resolution at which games display is up to the developer that creates the game. Often performance issues and hardware limitations force developers to render games in 720p rather than 1080p. This might seem like a reduction in visual quality, but often it benefits the overall game by increasing the performance.
The maximum resolution for a game will be listed on the back of the game box. The majority of games will be in 720p which means you will not be able to play the game in 1080p natively. It may be possible to force the game to output in 1080p, but this will just be up-scaled and often results in a reduction in picture quality. The general idea is, if the developer has limited the resolution of a game then it was done for a reason.
If a game supports 1080p, but is displaying in 720p or less there are a few things that you need to check. First make sure you are using HDMI or component cables. The cables that come with the Ps3 (yellow, blue and white) do not support HD. You will need to get a HDMI cable or Component cables to get a HD picture. If you are using HDMI or component, then check the PS3s video output settings. Run through the wizard and make sure that the system is outputting a video signal in HD.
If you have done all this and it still isn’t outputting in HD you might need to check if your TV supports HD. Not all flat LCD TVs are high definition so make sure that the Tv you are using is HD.