It is defined using an IDCAMS command DEFINE GENERATIONDATAGROUP or DEF GDG for short. Not many parameters just a maxgeneration as I recall.
If you create a GDG called MY.GDG this first instance will be cataloged as MY.GDG.G00001V00 and onwards. Each time you reference one you can do so by absolute reference as above or relative. MY.GDG(0) which is the most recent generation. MY.GDG(-1) is the next oldest and so on.
To create a new GDG generation you code in your JCL ..DSN MY.GDG(+1) DISP (NEW CATLG) etc as normal. Whatever you created as a max generations the last one gets dropped off (uncataloged and deleted) assuming you have that many generations.
They are useful for backups and the like. If you run a particular batch job on a daily basis then its often the case that you have a 5 generation (or 7?!) GDG to capture your output or parameters etc. You then have a week to print them or reference them.