In the Old Testament, anointing with oil was used ceremonially to set apart special roles, especially those of prophets (1 Kgs. 19:16), priests (Ex. 28:41), and kings (1 Sam. 9:16).
The most common Hebrew word for "anoint" is mashah, from which will come the term Messiah. The Greek word for "anoint" is chrio. The word "Christ" derives from that root word.
Jesus becomes the "anointed One" (see Acts 10:38) because in him is happily combined the roles of the prophet (Jn. 4:19; Acts 3:22ff), priest (Zech. 6:12-13; Heb. 3:1), and king (Mt. 2:2; Lk. 1:32-33; Acts 2:30ff). As prophet, Christ is the spokesman for God (Jn. 1:18). As priest, he offered his blood for atonement (Heb. 9:14). As king, he reigns at the right hand of God (1 Pet. 3:22).
