A turbulent history

Over the past three decades, spacecrafts have shown us that Mars is rocky, cold, and dry beneath its hazy, pink sky. Evidence from Mars missions suggest Mars may have been much warmer and wetter than we observe it to be today. An early clue was this huge shield volcano about 26 kilometers high and 600 kilometers across; has about the same area as Arizona. Known as Olympus Mons.
Mars' highest point: Olympus Mons. Image: NASA/JPL-Caltec
We've discovered that today's Martian wasteland hints at a formerly volatile world where volcanoes once raged, meteors plowed deep craters, and flash floods rushed over the land. For example, the canyon system of Valles Marineris is largest and deepest known in solar system; extends more than 4,000 kilometers and up to 10 kilometers deep.
Valles Marineris image from Mariner 9. Image: NASA/JPL-Caltech
Because water is key to life as we know it, NASA designed earlier Mars missions to make discoveries under the science theme of "Follow the Water." Alluvial fans identified on Mars are one of the more definitive evidences for liquid water flowing on the Martian surface and preserve information about the hydrologic conditions at the time of their formation. For example these channels are throught to have formed millions of years ago:
Channels carved by flooding on Mars millions of years ago. Image: NASA/JPL-Caltech
Progressive discoveries related to evidence of past and present water in the geologic record make it possible to take the next steps toward finding evidence of past habitable environments and possibly life itself. The Mars Science Laboratory mission and its Curiosity rover mark a transition between the themes of "follow the water" and ”explore habitability”/”Seek Signs of Life”. While doing so, it continues to prepare us for human exploration by understanding more about hazards in the Martian environment.
Image: NASA
In addition to landing in a place with past evidence of water, Curiosity is exploring past habitability and seeking evidence of organics, the chemical building blocks of life.

Why do we look for organics?

Since Curiosity found habitable conditions favorable to life in the first year of its mission and continues to see special clays that are known on Earth to preserve organics, its findings can shape future missions that would potentially bring samples back to Earth for life-detection and other tests or for future missions that carry advanced ancient-life-detection experiments to Mars.
In this sense, NASA’s Curiosity rover is on the cusp of a strategic transition in Mars exploration science strategies, establishing habitability and paving the way for seeking signs of life with future missions.  While it cannot detect signs of past life itself, it is part of a step-by-step exploration plan to make progress in that direction.

Mission objectives

Biological objectives: Inventory organic compounds which are the chemical building blocks of life (carbon, hydrogen, nitrogen, oxygen, phosphorous, and sulfur)
Geological and geochemical objectives: How were rocks formed over time? What are they composed of?
Planetary process objectives: History of Martian atmosphere. Assess long-timescale (i.e., 4-billion-year) atmospheric evolution.
Surface radiation objective: How much shielding would humans need? Characterize the broad spectrum of surface radiation.