Static stability basically means, if your flight condition is disturbed (e.g. by a gust) the aircraft returns to the initial state. This happens very quickly, and only extremely exceptionally skilled pilots (or clever computers, like on the Eurofighter) could do this manually. Normally you expect the aircraft to do this entirely by itself.
Dynamic stability means after returning to the initial state, the overcorrection is small, resulting again in a deviation in the other direction, which returns to the initial state and then swings back to the first disturbed condition. If those oscilations around the initial state fade, the aircraft is dynamically stable. If those oscilations do increase, the aircraft is dynamically instable. Typically a pilot (or a conventional autopilot) can dampen this out, so light dynamic instability is not unusual.
You may google Phygoid to learn more about it.