Picture someone about to say something, and in the half-second before they speak they smooth the edges off it: they add please, they wait for their turn, they say sorry as they squeeze past. Polite is that smoothing — the small adjustments a person makes so the other person is not bumped. Two things sit inside the word from the start: care about how the other person feels, and knowing the local rules for showing it. Most of the time those two travel together; the rest of the word's meanings appear when they come apart.