In the old covenant, the sacrifices were a type of the coming sacrifice of the Messiah, our Lord Jesus. A pure animal was selected, set apart, killed and offered up to God on an altar. In this the priest was enacting a type, a foreshadowing, of the coming propitiation accomplished by Christ when He was offered up to God. The sacramental offerings of the Old Testament were therefore a type of propitiation—an offering to God.
This Supper is also a sacramental sacrifice, but there is a marked difference. There the sacrifices were offered, and offered repeatedly. Here the sacrifice is received. God is giving to us. Our sacrifice here, therefore, is not a sacrifice of propitiation, but is rather a sacrifice of returned praise and thanksgiving. We receive at a Table; we do not offer upon an Altar.
The Greek word for rendering such thanks is the verb eucharisto, from which we get the Word Eucharist. In Hebrews 13:16, the apostle tells us to do good, and not to forget to communicate. By this, he does not mean communication in our sense of the word—i.e. talking. The word here is koinonia, the partaking of the Lord’s body that is accomplished in our observance of this Supper. A better rendering would be “do not forget to come to communion.” In the previous verse, he says something contextually telling. He says that we are to offer up sacrifice of praise, the fruit of our lips giving thanks to His name (v. 15).
This is the altar we have, and from which we eat. The altar is the altar of grace, established once for all two thousand years ago, and when we eat by faith, we overflow in Eucharistic thanks and praise.