If you resume something, you start it again after stopping. You might resume singing an aria after breaking to spit out your gum.
Resume is from Latin resumere "to take up again, take back," from the prefix re- "again" plus sumere "to take up, take." The Latin verb sumere is formed from the prefix sub- "under, up" plus emere "to take." When you pause a movie or game and then you press play again, what you're really doing is resuming play.