It's when you turn your phone into a portable wifi hotspot (essentially you convert the 3g connection your phone can use into a wifi signal). Any wifi enabled device will see your phone as a wifi point and be able to connect to the internet via the phone. Depending on your smart phone 'flavor' and carrier, some devices allow this, others do not.
Normally 'rooting' or 'jail breaking' your phone will allow you to run an app that will let you do this even if you carrier blocks it out of the factory.
When you do this it will allow you to use the phone as normal (calls and sms) but obviously it can't connect to wifi at the same time, but it does use more battery juice and can eat into data usage depending on what you are tethering.
The advantage of this is that you only need one data package (on your smart phone) that you can connect all your peripheral devices to (such as the Vita, an iPad, iPod touch etc) and you can also buy the normally cheaper wifi only variant of said hardware.
(Hope that clears that up )
For me, getting the cheaper wifi only model is no-brainer. I have a wifi/3g iPad and have never put a sim card in it. I can't justify the cost of a second data plan when I have such a good plan for my phone that I can share.