He refers to the tabernacle or the temple of the Jewish era. Under the law of Moses the one making the offering and the priests were allowed to eat part of certain sacrifices offered up to God (Leviticus 6:16; 23, 26).
Where is our altar? If you have advanced at all in doctrine, the answer to that question will have come into your mind, without any doubt. If you are a Christian, a child of God, and you need to deepen and learn, then you would have thought to yourself, what is the answer to that question? Where is our altar? It is not in the church, of course. Then where is it? Christ is our altar. That is the point of the passage. It is talking about Christ. The Christian’s altar is a person, the glorious Son of God, Jesus Christ; he is our altar. He is the one who has personally made the great sacrifice, and taken the punishment of sin for me. He is the one through whom we come to God to worship. Through him we worship; we pray all our prayers in the name of Jesus Christ, because he has purchased our right to be heard. He is our double altar. He is the altar of sacrifice, but there was another altar located within the tabernacle of ancient times. It was the golden altar on which the incense was burned, filling the place with the aroma and the smoke that represented the presence of God and communion with him, and the ascent of prayers to God. Christ is our double altar. He is our sacrifice, and he is our access to God. He is the one who carries our prayers into the presence of the Father. He is everything to us. He is the one of whom we learn first and foremost. He is the one to whom we commit ourselves. He is the altar on which we sacrifice our poor unworthy lives, giving ourselves entirely to him, and he is our nourishment.
We should never call the Lord's Table, an altar. Even some of the reformers made a mistake, when, at the time of the Reformation in the Church of England, they continued referring to an altar, the Lord's Table. The Bible never calls the Lord's Table an altar. When the writer says here that we have an altar, he is referring to Christ and Calvary and his atoning death. There is no altar. It is the Church of Rome that calls it an altar and in the mass they claim to offer up Christ, in a sense, all over again and that is a blasphemy. Our altar is not made with human hands; it is in heaven, not on earth. We do not need to earthly types and figures anymore because Christ, the reality, has come, and to revert back to physical pictures is to deny that.