The wikipedia entry is excellent.
I think the essence of WiMax and what it means to the end user is being missed here.
It's a catchy buzz-word, and 'Max' brings to mind images of up-sized fast-food Internet access...
It's no 'magic bullet' for bandwidth-starved South Africans, but purely a cost-effective last-mile solution to deliver 'broadband' to the masses.
In terms of sheer performance, there's no doubt that cable (or fibre) is king. Nothing beats good old copper at the end of the day. Wireless service delivery is probably as susceptible to disruption by environmental factors as copper is to cable theft. Each has their pros and cons in stability, portability, consistency and performance.
I've been extensively involved in WiFi service delivery, and been in on tests of four different manufacturer's 'WiMax' base-station deployments.
My real world experience so far, as well as monitoring about 150 users', is that in reality a user can expect anywhere between 20-120ms additional latency just to the base-station. Different manufacturer's use different ways of managing the contention on the sector (another key WiMax feature), and even a lightly-loaded base can add as much as 120ms. What that's connected to - fibre, more wireless links, copper - will more than likely add a bit more. Connection speeds to to the tower are definitely not 100Mbps!

Typical maximum speeds are anywhere between 1Mbps to 10Mbps to the tower - depending on make, distance from the tower & quality of the signal. Your Internet connection speed depends on the package - same as any other medium. Individual sectors can typically deliver around 6Mbps to 10Mbps in total, potentially shared between around 500 or more users. A single cell site would typically have a number efficient sectors, so it's not as bad as it sounds.
Note that a WiMax base station could be run off an ADSL line, so extending the range of any network is really what it means in the broadband market, and should be viewed as such. Expectations by users of wireless products may sometimes be a little high as the next best thing starts gaining ground, but I think it's essence is about deploying efficient technology and providing convent access for more users.