HSDPA stands for High-Speed Downlink Packet Access.
It's a fast 3G network used by AT&T and T-Mobile. HSDPA is the fastest of the fast 3G networks; it's so fast that it's often called a 3.5G network.
AT&T says its HSDPA network can hit speeds of 3.6 Mbps to 14.4 Mbps. Real-world speeds typically are slower than that, but HSDPA is still a super-fast network.