As stated on the MSL website, the mission is to determine the "habitability" of Mars, both now and in the past.

The objectives are:

1.Determine the mineralogical composition of the Martian surface and near-surface geological materials.

2.Attempt to detect chemical building blocks of life (biosignatures).

3.Interpret the processes that have formed and modified rocks and soils.

4.Assess long-timescale (i.e., 4-billion-year) Martian atmospheric evolution processes.

5.Determine present state, distribution, and cycling of water and carbon dioxide.

6.Characterize the broad spectrum of surface radiation, including galactic radiation, cosmic radiation, solar proton events and secondary neutrons.

From http://en.wikipedia.org/wiki/Mars_Science_Laboratory