a permanent holding: land (or property) held in lasting, heritable ownership
Achuzzah names something a person or group owns and keeps, with the ownership treated as settled and passed down rather than temporary. It comes from the verb meaning to grasp or take firm hold, so the picture is of something seized and kept fast. In practice the word is almost always about land: the family's allotted piece of ground, held in perpetuity and handed on to the next generation.
The senses below are not different meanings so much as the same idea seen in different settings. The core is always a secure, lasting holding. What shifts is what is held and how: a clan's farmland and towns, a grave bought to bury one's dead, even purchased servants counted as lasting property, or, in one royal poem, the nations themselves given to the king as his to keep.
The land laws of Leviticus and Numbers give the word much of its weight. Israel's land was understood as God's gift, parceled out by tribe and family, and an achuzzah could not be sold off forever: in the Jubilee year it returned to the family that originally held it. So the word carries an idea of ownership that is real and defensible yet still answerable to God, who remains the true owner of the land.