I think by cure they mean eradicate the virus, rather than suppress it. Most people can live relatively normal lives by keeping their viral load low, but this involves taking expensive medications every day for the rest of one's life. The drugs are things like protease inhibitors, modified DNA bases, etc. that muck up the virus' replication machinery so that it cannot make more copies.

The goal of a lot of researchers is basically an HIV antimicrobial that kills the virus in the same way you might treat pneumonia, so that maintenance therapy is not needed.