Its off road riding on motorbikes, except rather than having to pay a small fortune to go to an off road center or course you go on unused roads
Different counties have more than others, it depends what the council class them as to whether legally you can ride on it or not.
I think the general idea is you get very muddy and don't care.
Green lanes are open to all road registered motorised vehicles (as they are in fact simply unmade roads with vehicular access) as well as bicycles and ramblers etc.
There seem to be remarkably few around the Stafford area that are suitable for motorised vehicles. There used to be a few good ones across the Chase. The only meaningful one I can find runs from Whitgreave across to the Eccleshall Road in Stone. However, I have heard that that
may have been blocked up at the Stone end. There is also one that runs from the the A51 across to Ingestre, though the locals don't like people using it and it is flat and very boring. For anything of any length or challenge then your best bet is the Peak District, where there are loads. Don't know what the situation is in Shropshire though.
As Henryscat suggests, your best source of information is an up-to-date OS map. They have the green lanes marked on them. There are a few websites that will charge you for the information, but they tend to be out of date.
If you're going to use green lanes then please respect all other users, including pedestrians as they have just as much right to be there as you on a bike or me in a 4x4.
Try this as a starting point
http://footpathmaps.com/