"I desire the bread of God, the heavenly bread, the bread of life --- which is the flesh of Jesus Christ, the Son of God. . . . And I desire the drink of God, namely his blood, which is incorruptible love and eternal life."
The Lord's Supper is more than a memorial. The sign (bread and wine) is joined to the thing signified (Christ's body and blood), and thus we are given Christ's body and blood in the Supper, and through these, the benefits of Christ. How this happens is a mystery. What is important is that we do not merely receive the sign, but hunger and thirst to receive what the sign signifies.
The second quote of Ignatius, points to another important truth about the Lord's Supper:
"Let that be deemed a proper Eucharist, which is [administered] either by the bishop or by one to whom he has entrusted it."
The bishop was the pastor. The pastor usually administered the sacrament. But notice that the pastor could entrust this administering of the sacrament to others, who were not pastors. This is an important point if we are ever to return to a weekly or even more frequent partaking of the Supper. We must see that just as lay people can be licenced to preach, so lay people can be trained to administer the Lord's Supper. If we are ever going to return to the apostolic pattern of at least weekly communion, then more people must be trained and entrusted to administer it.