The D7000 has the focus motor in the body that will allow that lens to auto-focus. The D3000 (3100/3200) do not, nor does the D5000 (5100.)

That lens will auto-focus on the D7000.

In Nikon-speak, AF means the camera drives the focus, AF-S means the lens has the focus motor built in. AF goes back to the original auto-focus film cameras and the earlier digital SLRs, AF-S was introduced several years ago, and lower-priced bodies use those lenses. The more expensive bodies retain the focus motor for full compatibility with AF lenses.