On newer mobile phones, usually smart phones, they have 3G connectivity (As long as it's available in your area/offered by your cell provider). To be simple 3G is a fast internet connection for your phone, and 4G is it's successor. 4G promises to be significantly faster than 3G. 4G isn't "mainstream" yet or offered in many areas though.
That's all I know, anyone who knows more can feel free to correct me if I got anything wrong.
3G is the current generation of mobile telecommunication standards. It allows simultaneous use of speech and data services and offers data rates of up to 14 Mbps downlink and 5 Mbps uplink. 3G networks function with circuit /packetbased networks,so data can be transferred via both wired and wireless networks.
4G is the fourth and the next generation of mobile telecommunication standards. Its infrastructure will be only packet-based (all-IP). 4G will probably combine 3G, GSM, Wi-Fi, Bluetooth, and VoIP, which means it will be a completely wireless technology.
So 4G is Wimax? I read about wimax a few months ago and it is like a wide area wi-fi. A single mast can have a range of 30 miles and everyone within range will be able to have a wireless super-fast internet. They built one about 40 miles away from here, but they want silly money to subscribe (I'm outwith their reach anyway). I think the idea is that in cities the one mast will supply everyone and in that case it may well be free.