Spirit is one of the primary attributes that all characters possess.
The health regeneration provided by Spirit is not active while in combat, with the Troll racial ability Regeneration being the exception. The exact formula for this health regeneration is unknown, but the amount healed is considered negligible, especially for endgame situations.
The formulas and calculations for the mana regeneration provided by Spirit are a little complicated to sum up briefly.
For the mechanics, formulas, and details that go into them, see this informative article: Mana Regeneration.