I think Matthew Henry's Commentary answers your question best:
It is not so much an abuse of the body as of somewhat else, as of wine by the drunkard, food by the glutton, etc. Nor does it give the power of the body to another person. Nor does it so much tend to the reproach of the body and render it vile. This sin is in a peculiar manner styled uncleanness, pollution, because no sin has so much external turpitude in it, especially in a Christian. He sins against his own body; he defiles it, he degrades it, making it one with the body of that vile creature with whom he sins.
Also, the New Interpreter's One-Volume Commentary on the Bible goes into further detail on the context in Corinth for Paul's writing:
On the basis of OT teaching (e.g. Gen. 2:24, quoted in vs. 16), reaffirmed by Jesus (Mark 10:2-12), he believes that sexual intercourse is not an inconsequential, isolated act but one uniting man and woman in an intimate, complete, and enduring bond. Consequently he is revolted by the thought that a member of Christ's body should ever be united with the body of a prostitute. In Corinth, most of the prostitutes were slave women attached to the service of a pagan temple. It was commonly thought that any man having sexual relations with with these sacred prostitutes entered into communion with the god whom they served (cf 10:18-22)
Finally, I feel Proverbs 6:32-33 sums it up very succinctly:
He who commits adultery lacks sense; he who does it destroys himself. He will get wounds and dishonor, and his disgrace will not be wiped away.