I keep forgetting how consensus works, so this is me writing it down in the words that made it stick — less precise than the paper, more durable in my head.
One leader, one term
Raft's trick is to make one node the leader for a numbered term. Everything flows through the leader, so instead of agreeing on values you only have to agree on who's in charge.
Elections happen on a timeout. If followers stop hearing from the leader, someone times out, bumps the term, and asks for votes. A majority makes it official.
Why a majority
Because any two majorities of the same cluster must overlap in at least one node — and that overlap is what stops two leaders from both thinking they won.
Most of distributed systems is just 'a majority must overlap', repeated in clever costumes.