Hello kevsunuk, and welcome to WordReference.
In the UK, drivers get "penalty points" for motoring offences. Click Here.
Many advertisements for driving jobs have a requirement such as you have quoted.
As far as I know there is no legal definition of "minor points", but looking at the list, I expect that points for CD50 Causing death by careless driving when unfit through drugs are not minor points.
Points for CU30 Using a vehicle with defective tyre(s) probably are.
We use points in the US too. I've never heard the phrase "full clean driving license", just "clean driving license," but I think they mean that there must be no points on your record. Most of the time, if you just have a few points (I think 3 or less, which would be for minor traffic violations like running a stop sign, and they drop off after a couple years), they disregard them, but this employer won't tolerate any points.