In the simplest of terms WiMAX is a form of wireless broadband.
There are two forms of WiMAX. The first is 802.16d, which is a fixed WiMAX offering. Fixed WiMAX consists of a base station providing network coverage to an area and a transmitter/receiver installed at the end users location (home / work place). The second version is 802.16e, which is a mobile WiMAX offering. This works in a similar way to fixed WiMAX, but the end user is not fixed to a single location. They can use their laptop or similar WiMAX enabled device on the go within the coverage area.
With the development of VoIP technology both WiMAX versions are challengers to traditional fixed line and cellular services.