The word Christ means "anointed" in Greek. The Hebrew word for "anointed" is Messiah. So when we use the words Christ or Messiah, we're referring to an anointed one, and in particular, the anointed one that God had promised in the Old Testament. Where is the Anointed One promised in the Old Testament?
In the Old Testament, there are three types of people who were anointed:
The priest (often called "the anointed priest" - Leviticus 4:3, 4:5, 4:16, 6:22)
After freeing Israel from slavery in the land of Egypt, God brought them to Mt Sinai where He made a covenant with them. And God called Moses to come up into the mountain, where God gave Moses the 10 Commandments written on stone and instructions for building God a sanctuary "that I may dwell among them" (Exodus 25:8). This sanctuary was the Tabernacle. It was the place where God dwelt among the people. His presence was there. It was the place of worship where the 10 Commandments were stored and where sacrifices were offered to atone for sin and to thank God. God appointed priests to serve at the Tabernacle. "You shall anoint [Aaron and his sons], consecrate them, and sanctify them, that they may minister to Me as priests." Exodus 28:41b The priests were anointed with holy oil, oil which was only used to anoint the holy objects and people of the Tabernacle (Exodus 29:7, 30:23-33). Psalm 133 speaks of the beauty of this anointing, comparing it to "how good and how pleasant it is for brethren to dwell together in unity! It is like the precious oil upon the head, running down on the beard, the beard of Aaron, running down on the edge of his garments."
The prophets (1 Chronicles 16:22; Psalm 105:15)
The Bible records one event where a prophet was anointed. God commanded Elijah to anointed Elisha as prophet in his place (1 Kings 19:16).
The king (often simply called "His anointed" - 1 Samuel 2:10, 12:3, 12:5, 16:6, 24:6, 24:10, 26:9, 26:11, 26:16, 26:23; 2 Samuel 1:14, 1:16, 19:21, 22:51, 23:1; 2 Chronicles 6:42; Psalm 2:2, 18:50, 89:38, 89:51, 132:10, 132:17)
A few hundred years after the Exodus, Israel asked for a king and God gave them one. God spoke to the priest Samuel and told him, "Tomorrow about this time I will send you a man from the land of Benjamin, and you shall anoint him commander over My people Israel, that he may save My people from the hand of the Philistines; for I have looked upon My people, because their cry has come to Me." (1 Samuel 9:16) "Then Samuel took a flask of oil and poured it on [Saul's] head, and kissed him and said: 'Is it not because the LORD has anointed you commander over His inheritance?'" (1 Samuel 10:1) Later, David was anointed by Samuel with a horn of oil and made king in place of Saul. When this happened, the Spirit of the LORD came upon David. Other kings in Israel's history were also anointed with oil: Solomon (1 Kings 1:39), Joash (2 Kings 11:12), etc.
There is another aspect to the anointed king that needs to be seen. This is the promise that God made to David, saying that "When your days are fulfilled and you rest with your fathers, I will set up your seed after you, who will come from your body, and I will establish his kingdom. He shall build a house for My name, and I will establish the throne of his kingdom forever..." (2 Samuel 7:12-16). God promised to give David a descendant who would build God's house and whose kingdom would endure forever. This is the Anointed One (or Messiah in Hebrew, or Christ in Greek) whom Daniel prophesied of: "Know therefore and understand, that from the going forth of the command To restore and build Jerusalem Until Messiah the Prince, There shall be seven weeks and sixty-two weeks..." (Daniel 9:25-26) This is the Anointed One whom the people were expecting. Andrew went to his brother Peter and told him, "We have found the Messiah." (John 1:41) Also, the Samaritan woman at the well knew that Messiah was coming (John 4:25). Simeon, Peter, Martha, Samaritans, demons, and angels acknowledged that Jesus was the Messiah (Luke 2:26-30, Matthew 16:16, John 11:27, Luke 4:41, John 4:42). Many people cried out to Jesus, "Son of David!" (Matthew 15:22, 20:30-31, 21:9) The high priest demanded to know if Jesus was the Messiah (Matthew 26:63). John wrote the fourth gospel in order "that you may believe that Jesus is the Christ, the Son of God, and that believing you may have life in His name." John 20:31
"I have made a covenant with My chosen,
I have sworn to My servant David:
'Your seed I will establish forever,
And build up your throne to all generations.' Selah
And the heavens will praise Your wonders, O LORD..." Psalm 89:3-5