Boyd’s Bible Dictionary:
(bearing towards). Either bloody, as of animals, or bloodless, as of vegetables. They embraced the burnt, sin, trespass, peace, and meat offerings (Lev. 1-9).
Concise Bible Dictionary:
There were two distinct actions connected with the sacrifices. Any Israelite could bring an offering, or offer a gift, or a sacrifice; but only the priest could offer up the sacrifice on the altar to God. In the New Testament there are two Greek words translated “to offer.” One is προσφέρω, “to bring to,” “present.” This is used in Matthew 2:11, of the wise men who “presented” their gifts unto the Lord. So too vinegar was “offered” to the Lord on the cross (Luke 23:36). The word is referred to the Lord in Hebrews 9:14, 25,28 and Hebrews 10:12. The other word is ἀναφέρω, “to bring up,” and hence “to offer up.” In Matthew 17:1, Jesus “bringeth up” Peter; and in Luke 24:51 The Lord was “carried up” into heaven. This word is employed in Hebrews 7:27, both as to the high priest “offering up” sacrifices and to Jesus who “offered up” Himself. It occurs also in Mark 9:2; Hebrews 9:28; Hebrews 13:15; James 2:21 and 1 Peter 2:5,24.
In the LXX the word προσφέρω is mostly a translation of qarab, “to draw near,” which constantly occurs in Leviticus and Numbers in the laws respecting the offering of sacrifices, and is translated “to offer.” On the other hand ἀναφέρω is chiefly the rendering adopted for alah, “to ascend, to make to ascend.” The word alah is frequently translated “to offer,” but only twice in Leviticus (Lev. 14:20; Lev. 17:8); and four times in Numbers (Num. 23:2,4,14,30), when Balaam and Balak offered up sacrifices. Both Greek words are applied to Christ as to the offering of Himself (Heb. 9:14; Heb. 7:27). They are both also used of Abraham offering Isaac; he gave Isaac, and as a priest virtually offered him up (Heb. 11:17; James 2:21).