One of the crucial elements for life to be able to develop, at least in the form that we know it, carbon based, is the existence of water. One of the early measurements that the Curiosity rover made on Mars was to read the levels of methane gas on the panet. The measurement proved reassuring at first, but, later, the measurements showed that the concentration of methane was too weak to be local, and in fact it was methane brought from Earth to the planet.
In any case, even before Curiosity made its investigative debut, the previous missions who had seen the Viking Landers 1 and 2 proved that the soil contained traces of elements which under the right circumstances might be good for life development. At any rate, at the moment, Curiosity is functional, able to inspect the surface of the planet more closely and investigations seem to indicate that in the past there was life on Mars, even if in its primordial state, mono-cellular, similar to our bacterial Earth bound Life forms.
The planet has had water flowing in the past as its topology seems to suggest. There are river beds on the surface of the planet and further digging into these might uncover traces of life. The Curiosity rover is bound to give a definitive answer to this question and the fact that at them moment it is functional and able to continue its mission is a step in the right direction.
It the rover should fail to showcase some hard evidence of life, there is another hope coming from future rover missions, which might be more capable of digging the surface of the planet and uncovering its secrets from the depths. But, even Curiosity seems to be on the right path to discovering some very interesting facts about the planet, facts which might change our perception about how life has evolved in our solar system.