What does it mean when the Bible says, “You are a priest forever according to the order of Melchizedek (Hebrews)? I’ve heard he was an early appearance of Christ.

Melchizedek first appears in Genesis during the life of Abraham. This is what it says: Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High, and he blessed Abram, saying, “Blessed be Abram by God Most High, Creator of heaven and earth. And blessed be God Most High, who delivered your enemies into your hand.” Then Abram gave him a tenth of everything—Genesis 14:18-20. Then we next hear about him in Psalm 110, when David writes, The Lord has sworn and will not change his mind: “You are a priest forever, in the order of Melchizedek”—David, Psalm 110:4. Finally, in the New Testament book of Hebrews, he is referenced twice: And he says in another place, “YOU ARE A PRIEST FOREVER, IN THE ORDER OF MELCHIZEDEK.” During the days of Jesus’ life on earth, he offered up prayers and petitions with loud cries and tears to the one who could save him from death, and he was heard because of his reverent submission. Although he was a son, he learned obedience from what he suffered and, once made perfect, he became the source of eternal salvation for all who obey him and was designated by God to be high priest in the order of Melchizedek—Hebrews 5:6-10; and the entirety of Hebrews 7. The author of the book of Hebrews is making an argument to a Jewish audience, now become Christian, that Jesus is a better high priest than what they would have experienced through the line of Aaron, the line through which all high priests descended. To make this argument, the author goes back to the story from Abraham’s time of his encounter with Melchizedek. “Mel” was a real guy, who functioned as both priest and king in Salem (very early Jerusalem). But his biographical material is very limited; the author says so, noting that we don’t know when “Mel” was born or when he died—as if he were eternal (he wasn’t). In doing this, the author is practicing “typology,” which is using people or events in the Old Testament as models or examples that foreshadow events in the New Testament or, as is often the case, are fulfilled by Jesus Christ. For example, Christ used this Himself when He borrowed the story of Jonah from the Old Testament to illustrate Himself: Then some of the Pharisees and teachers of the law said to him, “Teacher, we want to see a miraculous sign from you.” He answered, “A wicked and adulterous generation asks for a miraculous sign! But none will be given it except the sign of the prophet Jonah. For as Jonah was three days and three nights in the belly of a huge fish, so the Son of Man will be three days and three nights in the heart of the earth—Matthew 12:38-40. Obviously, Jonah was not Christ, but his story presented an example useful for Christ in making His case before the Pharisees who were confronting Him. Now in this case, “Mel” fulfills this role in that he functioned as both a king (of Salem) and a “priest of God Most High,” thus showing himself to be better than the priests of the line of Aaron, who were priests only but never functioned as king—in fact, there were times where the king, particularly David, could subject the priests to his rule—in a sense, becoming a priest-king (such as when he led the procession of the Ark of the Covenant coming to Jerusalem (II Samuel 6). And with no birth or date, his life reflects in a sense eternity—as obviously Christ does. The argument concludes with the idea that Christ is a better high priest than any in Judaism: he is eternal (no need for multiple high priests), he is also king, and he gave a sacrifice once for all for all mankind. But “Mel” is not Christ; what you would have then is Christ being presented as an example of Christ. They are two distinct beings who the author of Hebrews was inspired by the Holy Spirit to use as an example in presenting the case for Christ as a superior high priest to anything the Jews had had before.
The idea of an early, or “pre-incarnate,” appearance of Christ is one version of what is called a “theophany.” In general, a theophany is an appearance by God where he takes on some form, usually a human one, in order to be seen by humans. It is sometimes argued that it may have been Christ who was one of the three visitors hosted by Abraham prior to the destruction of Sodom and Gomorrah (Genesis 18). It has been suggested that it was Christ that appeared with Shadrach, Meshach and Abednego in the fiery furnace in Babylon that started King Nebuchadnezzar so much (Daniel 3:25). The important thing to keep in mind is that a theophany only appears to be a human being whereas, in the incarnation, God became fully human in the person of Jesus Christ.