There are two types of wireless connections for your home. The first is Wireless Networking. This is a type of LAN which doesn't require the use of hubs to connect everyone to the same network. It's useful in houses where there's more than one desktop PC, and perhaps a laptop or two as well, as you don't need wires trailing all over the place. Wireless networking works by having a single central router that receives the signal from the telephone line and transmits a signal which is picked up by the closest wireless devices such as your home computers.
WiMAX is a protocol by which signals are sent to wireless broadband users. A WiMAX base station can theoretically beam a signal as far as 50km (31 miles), meaning that a single station could potentially cover an entire city (unlike Wi-Fi, which is only available in "hotspots").
Although WiMAX are networks are available in several major metropolitan areas in the US, base stations are very expensive to build, and aren't cost effective in less densely populated areas. Because of this limitation, WiMAX technology is not yet available in most non-urban regions.
Wireless broadband access is usually no slower than plugging the modem in directly, unless you have very cheap wireless equipment and a very fast Internet connection. It also gives you the added advantage that your computers will be networked together wirelessly, too - so you can easily make your folders shared and access them from any computer in your house using 'My Network Places'.