G2 is short for 'general 2'. It is used in reference to the graduated drivers licenses system in Ontario, Canada. When an any in Ontario turns 16 they can take a written test to get their G1. A G1 lets you drive only when someone who has had their G for 4 years (this could be wrong, but in any event they need to be experienced) in the passenger seat. In about 9 months or less if you take a driver's Ed courses. At this point you can go for your G2 in car test. A G2 is like a real licenses except you can't have any alcohol in your blood. When you turn 18 you can go for you G which is a real-no-strings-attached licenses.
There other types of licenses like M for motorcycles. For most of these you need to already have your G.