Trophies were added in a recent PlayStation 3 firmware update, allowing developers to reward players for their in-game accomplishments, similar to Xbox 360's achievements.
A few examples of the trophies were provided:
One Man Army
only those that are wily enough to survive a 6-star wanted level for a full 5 minutes will be rewarded with this one.
an award for those who find and execute all of the Unique Stunt Jumps throughout Liberty City.
an Achievement for those who can pull off blowing up 10 vehicles in 10 seconds or less.
Liberty City Minute
for those who have completed the game story in less than 30 hours. As the Social Club's Story Gang leaderboard can attest, this is not an easy feat.