The word "Christ" first appears in the New Testament in Matthew 1:1 and appears over 500 times. From the Greek "christos", the word means "anointed". To Anoint something or someone means to consecrate or make sacred, or to dedicate to the service of God. “Christ” is the Greek equivalent for the Hebrew word “Messiah.”
Jesus was a man, begotten by God's holy spirit to come to earth for a very specific purpose, to redeem all that was lost when Adam sinned. So the man Jesus was anointed, or dedicated to the service of God, for the purpose of saving mankind. While Jesus was a man, He was singularly focused on His purpose to do the will and works of his Father. He came to earth to offer his life in sacrifice to pay the ransom (corresponding price) for Adam, and all that were born in Adam.
The word "Christ" is used to describe the man Jesus, for he was anointed by God for a special service. Anywhere the word Christ is in the Bible, it may help to clarify the meaning of the verse by substituting the words: "(the) anointed". This could help explain the relationship between the words "Jesus" and "Christ". For example:
Matthew 1:16 And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called the anointed.
Mark 12:35 And Jesus answered and said, while he taught in the temple, How say the scribes that the anointed is the Son of David?
Luke 2:26 And it was revealed unto him by the Holy Ghost, that he should not see death, before he had seen the Lord’s anointed.