1 Kings 1:anointing32-40 ( KJV ) 32And king David said, Call me Zadok the priest, and Nathan the prophet, and Benaiah the son of Jehoiada. And they came before the king. 33The king also said unto them, Take with you the servants of your lord, and cause Solomon my son to ride upon mine own mule, and bring him down to Gihon: 34And let Zadok the priest and Nathan the prophet anoint him there king over Israel: and blow ye with the trumpet, and say, God save king Solomon. 35Then ye shall come up after him, that he may come and sit upon my throne; for he shall be king in my stead: and I have appointed him to be ruler over Israel and over Judah. 36And Benaiah the son of Jehoiada answered the king, and said, Amen: the LORD God of my lord the king say sotoo. 37As the LORD hath been with my lord the king, even so be he with Solomon, and make his throne greater than the throne of my lord king David. 38So Zadok the priest, and Nathan the prophet, and Benaiah the son of Jehoiada, and the Cherethites, and the Pelethites, went down, and caused Solomon to ride upon king David’s mule, and brought him to Gihon. 39And Zadok the priest took an horn of oil out of the tabernacle, and anointed Solomon. And they blew the trumpet; and all the people said, God save king Solomon. 40And all the people came up after him, and the people piped with pipes, and rejoiced with great joy, so that the earth rent with the sound of them.
This process of anointing the king with oil was also called unction. This process was not religious by any means; it was a governmental process of declaring that the man who received the anointing was the one that would ascend to the throne.  The one anointed had been declared the king, and this anointing was made public so that others were able to witness who would be next to sit upon the throne.  Additionally, the oil used to anoint the kings was called chrism, and it is from that word that the word Christ is derived.  So when the Lord Jesus asked Peter who did Peter say He was, Peter declared “you are the Christ,” meaning “you are the One anointed to ascend to the throne.”  Likewise, when we use the term “Christ,” we too are declaring that the Lord Jesus was the One anointed to receive the throne.  The thief on the cross recognized this as well, when he pleaded to the Lord Jesus “Lord, remember me when thou comest into thy kingdom.” The thief saw that the Lord Jesus was the One anointed to receive the kingly power, which is why the Lord bestowed great favor upon the thief in his last moments.  This is what it truly means to declare that Jesus is the Christ.