transition rate
A transition rate measures how quickly a quantum system tends to jump from one state to another. It answers the question 'how many such jumps happen per second?', and so it has the units of one over time. The faster the rate, the shorter the typical lifetime of the starting state before it gives way to the new one.
Rates are how the abrupt language of quantum jumps gets translated into something you can actually measure in a laboratory. You cannot predict the exact instant any single atom will decay — that is genuinely a matter of chance — but you can predict, with great precision, what fraction of a large collection will have decayed after a given time. The rate is the bridge between the unpredictable individual event and the smooth, reliable behaviour of the many.
A transition rate and a lifetime are two ways of saying the same thing: the lifetime is roughly the reciprocal of the rate. A large rate means a short-lived, quickly decaying state; a tiny rate means a long-lived, nearly stable one. Fermi's golden rule is the standard recipe for computing such rates from the underlying physics.
A constant rate Γ gives exponential decay; the lifetime is its reciprocal.
A constant transition rate produces exponential decay, but this is itself an approximation. At extremely short and extremely long times real quantum decay departs from a pure exponential — a subtlety usually negligible but real.