Leviticus 21 gives several laws for the priests, and we're told why: because "they present Jehovah's offerings by fire, the bread of their God" (Leviticus 21:6, 8, 17). That's an interesting phrase, "the bread of their God." It really means to food that God eats.
(We might find that strange. We eat because we need food to survive. If we don't eat, we die. God is eternal; He is self-sufficient – He doesn't need to eat. But Scripture says the offerings made by fire are God's food.)
The Lord Jesus takes up the idea of "the bread of God" in John 6:32. He talks about the bread of God being the One who came down from Heaven. And here it's not God who eats, but men and women who have no life in themselves (John 6:53).
There are two different ideas here: in Leviticus 21 we have "bread of God" meaning the food for God. In John 6 we have "bread of God" meaning the food from God. It shouldn't surprise us that those two ideas converge in Christ Jesus.
Christ offered Himself up to God (Hebrews 9:14). He says that God didn't really want sacrifices and offerings, He wanted to be glorified in the obedience – and eventual offering of the body – of Christ (Hebrews 10:5–10, quoting Psalm 40:6–8). Christ is the fulfillment of the Old Testament commands concerning offerings: it is Christ who is the true sweet savor (Ephesians 5:2).
At the same time, it was the Lord Jesus who came from Heaven to give His own body to be our food and His own blood to be our drink (John 6:49–57). He is the bread of God that came down to give life to the world (John 6:33). In fact, we find His body is the only food that can sustain eternal life, and His blood is the only drink for it (John 6:53). We not only get eternal life by eating His flesh, we sustain it the same way.
One thing John 6 brings to the forefront is the need for feeding as opposed merely to eating. There is certainly a one-time eating that gives us eternal life (John 6:53), but we find as well that there is a need to continue to feed on Him (John 6:56). It's easy to miss that.
I don't mean to be flippant, but it seems to me one of the lessons we can learn from Levitical law is that God doesn't like to eat alone. Numbers 18:8–14 tells us the priests were to eat from the sacrifices brought to God. There are some exceptions, but in general, the sacrifices included a portion for the priests.
Notice there are two categories in Numbers 18:8–13: vv. 8–10 detail the sacrifices that were to be eaten by the priests themselves, while vv. 11–13 tell us about the things that were to be eaten by the whole household of the priests. The sin offerings and the trespass offerings are limited to the priests, while the rest of the sacrifices were to be eaten by "every one that is clean in thy house."
We might think of those two categories applying to our feeding on Christ. There is an individual feeding [for just the priests], but there is a corporate feeding too [for everyone clean in the house]. We ought to be feeding on Christ in the assembly, and we ought to be feeding on Him in our individual lives as well.
I've heard many admonitions in various assemblies about not missing out on the meetings. We hear Hebrews 10:23–25 referenced a lot, but I'm not sure I've heard John 6 referenced in the same way. One of the reasons we gather is to feed on Christ as the assembly. This is the second eating in Numbers 18: it's the eating by everyone clean in the house.
But don't let's get into the idea that our only feeding is in the assembly. There is the need for the individual to feed as well. We do feed as the assembly, but we also feed as individuals. Notice John 6:53–58 doesn't reference a corporate setting, but a purely individual one.
Both the feedings are marked by the presence of God. Christ is the Bread of God. Do we think God isn't joining with us in feeding on Christ?
I was at a Bible Conference in Texas a few years ago, and in one of the Reading meetings, an older brother spoke up and said something like, "this is worship: sitting down at table with the Father, eating the food He eats." The more I examine passages like Numbers 18 and John 6, the more convinced I become that he put his finger exactly on what the Scripture teaches. God shares His Bread with us, and desires us to come and feed on it with Him.