The HIV virus attacks the T-Cells in your body when it goes to reproduce. A T-Cell's main job is to identify, directly attack, and destroy infectious agents. When the virus uses those cells to reproduce, it damages the T-Cell to the point where they can no longer to their job within our immune system.
Eventually it destroys so many cells that your immune system is no longer strong enough to fight off infection as disease.

So it isn't so much HIV itself making you sick, it weakens your immune system, allowing other illnesses and infections to make you sick.