Regeneration is a keyword action that is applied when a regeneration shield is used. When a permanent regenerates, it has all damage removed from it, it becomes tapped and remains in play. It is important to remember that this regenerated permanent is the same object. It does not leave the battlefield and then reenter. Because of this abilities that trigger when a permanent enters or leaves the battlefield will not trigger. Neither of the abilities of a Suture Priest will trigger when a creature regenerates.

Additionally, because it does not leave the zone it is in, any auras or equipment that are attached to it will remain on it. For example, if a River Boa is enchanted by Lifelink and equipped by a Trusty Machete and would be destroyed, both the aura and equipment will remain on it.

The one thing that a creature does leave is combat. An attacking or blocking creature that regenerates will be removed from combat. (Keep in mind that an attacking creature that blocked by it will still be blocked.)

To recap, a regenerating creature does not leave play, it does not leave its ‘stuff’ but it does leave combat.