Missions is one type of TBS fight. The other type is TBS Skirmish.
TBS Missions are designed for players to have to complete objectives and get nice rewards for completing those objectives. For example, you may be asked to kill specific monsters, gain territory, complete land and sea battles or free captives.
TBS Missions can take 20 minutes to over an hour to complete.
Completing several TBS Missions is required to complete the Main Character Level 130 Upgrade Quest.
Players will sometimes request that someone help them start a party so that they can form a squad, which is required for some things, like running TBS Missions in squad mode (which usually has better rewards than solo mode). If that player is a friend or in your guild or nation, it's nice to help that player out.