What is meant by the pre-existence of Christ?

Christ existed before He was born of Mary. Preexistence implies something existed before something else. The word "before" implies time. Time is a crucial part of this question. In 1971 it was proven that time varies with mass, acceleration, and gravity, and is therefore a physical property. Being a physical property, it was created. According to John 1:3, Christ created time.

All things were made by him; and without him was not any thing made that was made.

John 1:3 KJV

If Christ created time, He must have existed before time. Having created time, Christ must also exist outside of the boundaries of time. If you're still with me, the rest is very easy to understand. According to John 1:1, Christ existed in the beginning.

In the beginning was the Word, and the Word was with God, and the Word was God.

John 1:1 KJV

The beginning of what? Logically speaking, if Christ made all things that were made, then the answer is everything. John is not the only one who claimed Christ existed before he was born. This was foretold in the Old Testament.

But thou, Bethlehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth unto me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting.

Micah 5:2 KJV

For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counseller, The mighty God, The everlasting Father, The Prince of Peace.

Isaiah 9:6 KJV

The word everlasting means lasting or enduring through all time - eternal. It is common for people to assume this means from now on, but that is incorrect according to the definition of the word.

Zechariah recorded the promise that Messiah would come. According to Zechariah, he was told this by Messiah Himself. This promise clearly predates the birth of Jesus by Mary.

Sing and rejoice, O daughter of Zion: for, lo, I come, and I will dwell in the midst of thee, saith the LORD. And many nations shall be joined to the LORD in that day, and shall be my people: and I will dwell in the midst of thee, and thou shalt know that the LORD of hosts hath sent me unto thee.

Zechariah 2:10-11 KJV

In the book of John, Jesus said he predated Abraham.

Your father Abraham rejoiced to see my day: and he saw it, and was glad. Then said the Jews unto him, Thou art not yet fifty years old, and hast thou seen Abraham? Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am.

John 8:56-58 KJV

Later in the book of John, Christ Himself said he existed before the world.

I have glorified thee on the earth: I have finished the work which thou gavest me to do. And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was.

John 17:4-5 KJV

The book of Colossians says that Christ created everything, and existed before all things.

Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son: In whom we have redemption through his blood, even the forgiveness of sins: Who is the image of the invisible God, the firstborn of every creature: For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him: And he is before all things, and by him all things consist.

Colossians 1:13-17 KJV

Both the New and Old Testament show that the Messiah existed before He was born.