Boyd’s Bible Dictionary:

(fed). Forbidden food, as belonging to God (Lev. 3:3-17; 7:3,23; Neh. 8:10); yet fatted cattle enjoyed (1 Kings 4:23; Luke 15:23). Vat is meant (Joel 2:24; 3:13; Hag. 2:16).

Concise Bible Dictionary:

This portion of the sacrifices was to be burned on the altar. “All the fat is the Lord's. It shall be a perpetual statute for your generations throughout all your dwellings, that ye eat neither fat nor blood” (Lev. 3:16-17). Apparently, as to the fat, this refers to that "of ox, or of sheep, or of goat," the animals of sacrifice, and to the fat of any animal that died of itself, or was torn of beasts (Lev. 7:23-24). In Nehemiah 8:10 it was proclaimed, “eat the fat,” without any restriction; but here the Hebrew word is different, and refers more to “dainties.” In Isaiah 25:6 is another Hebrew word, and is “fat or rich things.” The “fat” signifies the best part, the inward energy and will: (Compare Num. 18:29 margin; Psalm 73:4 margin). It is typical of the inward energy of the Lord Jesus in the offering of Himself to God.