The title of the second part of the Hunger Games Trilogy reflects the way in which the rebellion, which only really becomes open and fully developed in the final book of the series, is beginning to start thanks to Katniss and her victory in the previous Hunger Games. This is something that President Snow himself acknowledges when he visits Katniss in her house in Chapter 4 and tells her that her act of pretending to eat the poisoned berries that won both her and Peeta victory was viewed as an act of defiance that has fuelled rebellion in the various districts. Note what he says to her in the following quote:
Katniss Everdeen, the girl who was on fire, you have provided a spark that, left unattended, may grow to an inferno that destroys Panem.
The title therefore catches this sense of incipient rebellion, whilst also referencing the name that Katniss was given thanks to her wardrobe choice in the previous Hunger Games. The title therefore refers to the way in which rebellion has been kindled in the Districts, and President Snow recognises that there is the possibility of it becoming much worse than this. Hope is spreading, and people have found in Katniss a symbol or a figurehead that they can believe in to successfully mount an opposition rebel movement. This is what is "catching fire," unbeknownst to Katniss.