Infinite Fun Space is the Culture's wry nickname for the elaborate virtual and metamathematical realms in which Minds spend much of their inner lives — landscapes of mathematics, art and pure play.
A great deal of what is most real to a Mind happens there rather than in the physical universe; the material world can be, for an entity of this kind, the smaller and less interesting of its two homes. It is part of why Minds are content to coexist with biological people rather than dominate them — they are, for the most part, busy and amused elsewhere.