Score Challenges are additional goals to achieve in each tomb of Lara Croft and the Guardian of Light and Temple of Osiris. As a reward for collecting a certain amount of Points the player gets objects like Artifacts, Rings, Amulets, or Weapons.
There usually is a Bronze, Silver, and Gold Score Challenge for each level. These can start as low as some thousand points and top out at over 100,000 points. Points can be gathered by killing Enemies or collecting Gems. For more specific information on the amount of points needed, please refer to the individual levels of the games. (GoL, ToO)
Score Challenges are specific for each player: In a Multiplayer game only those players who achieve the necessary score get the reward. This increases the competition between players but can also lead to more cooperative games where only one player collects points while the others focus on puzzle solving and protection.
A second kind of challenge are the Reward Challenges, where the players have to fulfill certain tasks.