It's from the twelfth episode of the original series, The Conscience of the King. It's part of Kirk Prime's backstory, and fandom has pretty much decided unanimously that it's too tempting a source of angst to not have it be part of reboot!Jim's backstory too. The actual canon details of what happened on Tarsus IV are pretty sparse, so everyone's got their own take on it, but the fungus wiping out the crops is canon, as is the resulting massacre (a man named Kodos seized power in the crisis and chose half the colony to die based on his own eugenics theories, and Kirk and eight other eyewitnesses survived). Help arrived earlier than Kodos expected, and he faked his own death and disappeared. Other than that, canon doesn't tell us much about the specifics.

Sorry if this posts multiple times; DW is giving me errors.