You are patient if you don't get frustrated or annoyed when you have to wait or deal with difficulties. The band director may show patient leadership, but a football coach uses other methods with his team.
It may be difficult to wait for something that takes a long time or deal with someone who is annoying, but if you are patient, you endure these things calmly and without frustration. Endure is the keyword here as patient comes from the Latin verb pati "to suffer, endure." Think of the patient way a chess player wins a game — calmly, steadily and willing to wait for the right time to act.