Jesus said to them, "I tell you the truth, unless you eat the flesh of the Son of Man and drink his blood, you have no life in you. Whoever eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. For my flesh is real food and my blood is real drink. Whoever eats my flesh and drinks my blood remains in me, and I in him. Just as the living Father sent me and I live because of the Father, so the one who feeds on me will live because of me. This is the bread that came down from heaven. Your forefathers ate manna and died, but he who feeds on this bread will live forever." (John 6:53-58)
What strikes me is that Jesus is telling us here what it means to walk with him. He calls us to be so close to him that we partake of him all the time. It's about intimacy: "into me see" (I got that from T.D. Jakes). It's about a fully open, fully accessible life.
Yes, we do communion or the Lord's Supper in remembrance of Him. Different Christians vary in how often they take communion and remember, but here in John, Jesus is saying that eating and drinking of Him is a continual practice, if we're walking with him. We're supposed to be communing with Him all the time.