The healing rate for a champion is equal to the level of the champion, plus any healing rate modifiers from equipment, spells, or traits (they will list +X health per turn, or something like that; an item with health regeneration is the Troll Charm, a trait that increases healing rates of everyone in the army is Healer, and a spell that increases health regeneration is Regeneration).
I believe unit healing rates are determined the same way as champion healing rates.