WiMax is Wireless Networking technology similar to Wi-Fi. However, where Wi-Fi creates a wireless network over a house, WiMax creates a wireless network over an entire city.
One huge disadvantage of WiMax over Wi-Fi is that, where with Wi-Fi anyone can set up a wireless network for free, not everyone is permitted to set up a WiMax wireless network; and one must pay incredibly huge amounts of money to be given the right to set up a WiMax wireless network in a region. In fact, governments give companies a monopoly to be the only one allowed to set up a WiMax wireless network in a region.
These companies who have been granted monopoly rights by the government to set up WiMax wireless networks in a region often become ISPs and charge people money so that they can access their WiMax wireless network and get Internet access.
One nefarious note: some telephone companies have payed the government to get the right to the WiMax networks in various regions for the sole reason of stopping anyone from setting up a WiMax wireless network. (In other words, they are doing this to try and stop WiMax everywhere.)
These infamous telephone companies are doing this for 2 reasons. #1: they do not want anything to compete with their mobile phone networks.
The usual business model for mobile phones companies is to nickel and dime you to death, changing you money for every single thing you do. WiMax would likely push VoIP into the mainsteam, and almost completely replace the telephone companies' telephone offerings. In other words, if WiMax was everywhere, everyone would likely get their phone for free (via telephone over the Internet -- VoIP).
And #2: To stop new competition to their DSL ISP service.
As time goes on, it is expected for WiMax network cards -- NICs -- to be built into virtually all computers, just as Wi-Fi NICs are built into virtually all computers today.