If a valid marriage never existed, what exactly does an annulment nullify?

An annulment is more accurately called a "declaration of matrimonial nullity," and it does not actually nullify anything. The process determines whether what appears to be a valid marriage really is one. If no valid marriage exists, it declares the marriage null: a valid marriage never existed.

In Annulments and the Catholic Church, Edward Peters describes it as a juridic determination that, at the time of the wedding, one or both parties lacked sufficient capacity for marriage, and/or one or both failed to give adequate consent to marriage as the Church understands it, and/or, where at least one party is Catholic, the parties violated the Church's requirements of canonical form.