You do your fights with a team of heroes: a team consists of one, two or three heroes selected by you using the Select team menu option. You can select any of the heroes available to you to join the team (some heroes need to be unlocked during the game).
When playing a quest, you will have to complete all the fights using the selected team, as you cannot switch heroes while in a quest (you can flee the quest, and start again with a difference team composition).
It is possible to do a quest (or any fight) with a team having one or two heroes. The advance of this is that any xp gained at the end of the fight is spread over a smaller group of heroes.