John 6:30-33 — They said therefore unto Him, "What sign showest Thou then, that we may see, and believe Thee? what dost thou work?
Our fathers did eat manna in the desert; as it is written, He gave them bread from heaven to eat."
Then Jesus said unto them, "Verily, verily, I say unto you, Moses gave you not that bread from heaven; but My Father giveth you the true bread from heaven.
For the bread of God is He which cometh down from heaven, and giveth life unto the world."
Jesus said "believe on Me," but they weren't ready even to simply believe Him (believe what He said). They demanded a sign — in spite of having seen Him feed the crowd the day before. For the Jews require a sign, and the Greeks seek after wisdom (1 Corinthians 1:22).
Their inference was that Jesus' miracle of feeding 5,000 was not as great as Moses' miracle of feeding manna to the entire nation of Israel.
Manna gives physical life temporarily, but the true bread from heaven (Jesus) gives spiritual and physical life forever.
Jesus explains that God, not Moses, brought the manna.
Their request for a sign and reference to Moses and manna sounds like they were just looking for another meal. "Feed us again, and then we will believe." Moses provided manna for 40 years — they also wanted a lifetime supply.
Manna — Then said the LORD unto Moses, "Behold, I will rain bread from heaven for you; and the people shall go out and gather a certain rate every day, that I may prove them, whether they will walk in my law, or no" (Exodus 16:4). And had rained down manna upon them to eat, and had given them of the corn of heaven. Man did eat angels' food: He sent them meat to the full (Psalm 78:24-25).
There was a tradition among the Jews that the Messiah would also cause manna to fall.
giveth life — the tense indicates a continuous giving of life. He keeps on giving.
True bread from heaven (verse 32) — real, genuine, satisfying, spiritual
Bread of God (verse 33) — Divine, eternal
Bread of life (verse 35) — gives and sustains life