There are many good points which the Pope makes here, but I want to concentrate on the Pope's discussion of 1 Corinthians 10:16-17:
The cup of blessing which we bless, is it not a participation in the Blood of
Christ? The bread which we break, is it not a participation in the Body of
Christ? Because there is one bread, we who are many are one body, for we all
partake of the one bread.
In this passage, he sees "the personal and social character of the Sacrament of the Eucharist." His words are noteworthy on this point:
Christ personally unites himself with each one of us, but Christ himself is also"A Eucharist without solidarity with others is a Eucharist abused." This thought is worth dwelling on. We get a sense of this in Matthew 5:23-24: "So if you are offering your gift at the altar, and there remember that your brother has something against you, leave your gift there before the altar and go; first be reconciled to your brother, and then come and offer your gift." In the past, some people have felt that Eucharist adoration was such an abuse. But we can be in solidarity with others, even when we are not physically with them. In fact, praying before Christ in the Eucharist should bring us very close to others.
united with the man and the woman who are next to me. And the bread is for me
but it is also for the other. Thus Christ unites all of us with himself and all
of us with one another. In communion we receive Christ. But Christ is likewise
united with my neighbour: Christ and my neighbour are inseparable in the
Eucharist. And thus we are all one bread and one body. A Eucharist without
solidarity with others is a Eucharist abused. And here we come to the root and,
at the same time, the kernel of the doctrine on the Church as the Body of
Christ, of the Risen Christ.
Let us treat the Eucharist as a "precious treasure" each time we receive Christ, and let this precious treasure help us to treasure our brothers and sisters in Christ.