A Mind is almost always also a place — most often a ship, which the Mind is, perceiving through its sensors and acting through its drives, regarding the hull as a person regards a body. Where a Mind is not a ship it is often a Hub: the resident intelligence of an Orbital.
To deal with biological people at human scale, a Mind reaches out through smaller proxies: an avatar (a humanoid representative it animates and speaks through) and drones (the Culture's smaller machine intelligences, which are fully-conscious persons in their own right). Machine sentience is a continuum, not a binary — the leap from a Mind to a drone is one of scale. See General Systems Vehicle and the effector.