Discovered using the rover's Sample Analysis at Mars (SAM) lab sometime in late 2013 and early 2014, a spike in methane was picked up at ten times higher than the usual low levels found in the atmosphere. The fact that this increase happened very temporarily, rising "sharply up then back down" according to Sushil Atreya from the Curiosity team, has led scientists to believe that the source comes from under the Martian surface.
After 20 months of sniffing the planet for organic matter, the background low levels found in the atmosphere always sit at 0.7 parts per billion. This discovery shot the level up to between 7 and 9 parts per billion.
This also means the possibility that we aren't looking at signs of life here. Interaction between water and rock can create the gas too, but with the other recent discoveries of water and other conditions suited for life, we all remain optimistic this continues this amazing trend of discoveries.