1 Chronicles 23–27 describes the distribution of responsibilities for the house of Yahweh (chs. 23–26) and the management of the king's palace and estates (ch. 27). Using lots, David and the priests create “divisions” of priests, Levites, singers, gatekeepers, treasurers, and others.
“Division” translates the Hebrew machaloqet, derived from the verb chalaq, “to apportion, allot.” It's used to describe the division of the land among the various tribes (Numbers 26:53-56; Joshua 13:7; 14:5; 18:2, 5, 10; etc.). The usage has an obvious literal justification: Some of the officers of David's court are actually given a “place” to work.
More metaphorically, David allots a set of responsibilities to his officials that are analogous to a landed inheritance. Like the land, the office requires work; the allotment of responsibility needs to be cultivated. And then Torah's regulations regarding land-care come into play to guide the office-holder in the conduct of his office.
Israel's farmers were forbidden to use their allotment simply to enrich themselves. They had to leave the edges of the land for the poor and stranger and passers-by; they made a profit from cultivating their land, but farming was a community service, intended to provide food for Israel as well as profit for the farmer. A tenth of all produce was offered to the Lord, an acknowledgement that Yahweh was the ultimate landlord and that all they produced came from Him and was ultimately at His disposal.
Mutatis mutandis, these directives applied equally to those who had been allotted an office rather than land. Public officials can, of course, milk their position to advance themselves, taking bribes and orchestrating law and policy to their own advantage. Israel's officers were warned not to take bribes, and the analogy with the cultivation of land points to the fact that public service is service to the public. Officers were given an allotment to enrich the lives of the people of Israel. Ultimately, the officer's plot, like the farmers, was a trust from God and had to be cultivated to honor Him.