A mission is a special quest, one that involves more effort than, say, a trip to the corner store. If you were to drive all around the state searching garage sales for porcelain cats, you could say you were on a mission.
Mission comes from a Latin word that means “to send.” It was first used by Jesuit missionaries who sent members of their order overseas to establish schools and churches. Foreign travel is still associated with the word. When diplomats and humanitarian workers travel abroad, we often refer to those trips as missions.