The noun form of succinct would be succinctness.
Brevity (briefness) just means the explanation is short. It might be ambiguous or vague, though.
Succinctness means that is explanation is clear and short.
What is a yellow jacket?
The brief answer= Some kind of bug.
The succinct answer = A wasp of the genera Vespula and Dolichovespula. Most have yellow and black stripes. (Ok, this could be shorter, but you get the idea.) :)