As this article explains,
The Christian altar is one of the earliest elements of the liturgy. In the first years when Christianity was illegal, the Eucharist was typically celebrated in the homes of the faithful. The altar could have been the dinner table in the home or the wooden chest in which a bishop would carry needed materials for celebrating the Eucharist from place to place.
Fixed altars made of stone became prevalent when Constantine established that Christianity would no longer be illegal and more churches were erected for the purpose of celebrating the Mass...
Early altars were not placed against walls, but set apart so that the bishop or priests would stand facing the people. Around the 5th century, it became popular for the altar to face the East or be set against a wall. The priest would celebrate the Mass facing east, and the people would face East with him, symbolic of looking toward Christ as the Dawn. In the Middle Ages, the altar ceased to resemble the table of the early Church. Altars of Medieval times began to be designed very ornately, and were adorned with statues, relics, and paintings, and of course the tabernacle. In the mid-20th century, in many countries, the altar was moved away from the wall again, with the priest celebrating the Mass facing the people.
As for the meaning behind the altar, it reaches back to Jewish times and the sacrifices done to atone for sins. Some Christians feel that such a thing is no longer relevant to Christians, but as we believe Christ didn't come to destroy the law, but to fulfill it, we see the Eucharist as the intended perfect sacrifice for which the Jewish peoples were prepared for so long.
The Catholic altar is both a sacrificial altar, and a table for a communal meal. In Jesus’s time, altars where animal sacrifices took place as atonement for sin were common under Jewish norms and traditions. The passion of Christ was the ultimate sacrifice, to atone for the sin of mankind. Therefore, the Christ’s sacrifice is enacted each Mass at an altar. The altar is also a table because we are all “called to the Lord’s supper.” The sense of the Catholic altar as a table calls to mind the last supper and the tables around which the early Christians celebrated the Eucharist, as well as the fact that we as a faithful community are sharing in the saving meal.
The altar is traditionally made of stone, calling to mind Christ as the living cornerstone of the Catholic faith:
“So then you are no longer strangers and sojourners, but you are fellow citizens with the saints and members of the household of God, built upon the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone” (Ephesians 2:19-20)
“Come to him, to that living stone, rejected by men but in God's sight chosen and precious; and like living stones be yourselves built into a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ. For it stands in scripture: "Behold, I am laying in Zion a stone, a cornerstone chosen and precious, and he who believes in him will not be put to shame.” (1 Peter 2:4-6)
Some more scripture related to altars:
Then Jeshua, son of Jozadak, together with his brethren the priests, and Zerubbabel, son of Shealtiel, together with his brethren, set about rebuilding the altar of the God of Israel in order to offer on it the holocausts prescribed in the law of Moses, the man of God. Despite their fear of the peoples of the land, they replaced the altar on its foundations and offered holocausts to the LORD on it, both morning and evening. (Ezra 3:2-3)
Do you not know that those who perform the temple services eat (what) belongs to the temple, and those who minister at the altar share in the sacrificial offerings?
In the same way, the Lord ordered that those who preach the gospel should live by the gospel. (1 Cor 9:13-14)
When he broke open the fifth seal, I saw underneath the altar the souls of those who had been slaughtered because of the witness they bore to the word of God. (Rev 6:9)
Another angel came and stood at the altar, holding a gold censer. He was given a great quantity of incense to offer, along with the prayers of all the holy ones, on the gold altar that was before the throne. (Rev 8:3)
Then the sixth angel blew his trumpet, and I heard a voice coming from the [four] horns of the gold altar before God (Rev 9:13)