I've been studying this transistor "latch" circuit over the past couple of days and I think I've grasped most of it, but I'm not sure about the purpose of capacitor C1.
If I understand correctly, the operation of the circuit is as follows: When the input is high Q1 turns on which in turn causes current to flow through the base of Q2 to the collector of Q1, turning Q2 on. Feedback to Q1's base from Q2's collector keeps Q1 turned on, which in turn maintains Q2 on.
As for the capacitor, I notice that if I don't include it sometimes the circuit won't latch, but I'm not 100% on the reason why. I thought perhaps the purpose of the capacitor was to allow Q2's base current to flow briefly in the event that Q1 is momentarily turned off?