means A layer of grass and the matted soil and roots holding it together — or, figuratively, the territory someone considers their own.

from From Old English 'turf,' meaning a slab of earth bound by grass roots, with deep Germanic roots and cousins across the old northern tongues (Old Norse 'torf,' Dutch 'turf'). Far back it may trace to a Proto-Indo-European root tied to 'to crumble' or 'powder.' For centuries 'turf' literally meant cut sods burned as fuel; the 'this is my territory' sense is a much later figurative stretch, borrowing the image of grass you've staked a claim to.