It means the death of Jesus Christ, together with the benefits which he obtained for us by his death. It is important to be clear about this because some people teach that 'the body and blood of Christ' mean his life, not his death. Since our body is the instrument of our personality, they argue, and since our blood is the carrier of life-giving oxygen, therefore Christ's body and blood together symbolize his living personality, and it is this that we receive at Communion. But this is not what Jesus himself said. Thus 'the body and blood of Christ' is a figure of speech for the benefits of his death, not for the power of his life.
Lutheran churches teach 'consubstantiation', which is somewhat similar.
The Anglican Articles reject this, however. Article 28 declares both that transubstantiation cannot be proved from Scripture, and that it overthrows the nature of a sacrament by confusing the sign with the thing signified. Article 29 says that those who lack a living faith, even though they receive the sacrament, 'yet in no wise are they partakers of Christ'. It is by faith, of which eating and drinking are a vivid picture. For just as by eating the bread and drinking the wine we take them into our bodies and assimilate them, so by faith we feed on Christ crucified in our hearts and make him our own.