Wimax is long range Wireless Network. It is basically a home wifi signal but on a much larger scale. Wimax is faster than wifi, you are no longer limited to how far your wifi signal can go, instead you can take it with you as long as you are in the coverage area.
Wimax is currently being offered in the USA by Clear.com. It is only available in select cities but you can check for coverage to see if your city/town is covered. Benefits of wimax is you are no longer attached to a plug in the wall, you can roam about any part of town without having to search for an ethernet plug or a wifi hotspot. As long as you are in the coverage area you will reap the benefits of wimax.
Big disadvantage is that it is not available in all areas, you will need to check coverage before you go about using the wimax service. Also wimax has a big competitor in LTE, which is another form of wireless network. LTE claims to be faster than wimax, however since no real production environments of LTE exists it is hard to compare against Clear's wimax service.
Verizon and other wireless carriers are on board with Wimax and plan to start deploying LTE networks in cities. Clear is testing out LTE service in Phoenix Arizona on a trial basis and LTE truly does take off, then Clear will most likely switch from wimax to LTE.