What's focus. Really, tell me pls

Focusing is like a mythological beast to me, something you heard of from many but never saw with your own eyes.
Whenever I decide to start my study session, even if I feel my willpower strong as a rock, i quickly lose everything, finding myself staring at the void of a white wall. My productivity has vanished and I don't know how it happened.
My sesh has became a deer-hunt , and my focus is that magical white deer with golden horns.
I'm not really in this critical situation, I like to exaggerate a little bit, sometimes I get to do my work done but is a delicate equilibrium of a thousand of factors, physhiological ones, wandering thoughts, crave of nicotine or, why not, the cute girl sitting next to me.
On the other hand during my pauses i can't really shut off my brain, and it continue working in background over the last problems, in fact is very common that in such moment i get the resolutive idea.
So, it's awkward, i would prefer to get a deep focus and a deep relax separately, like black and white, but all I got is a messy grey-ish mix, i'll call it "relork", or "workax", idk.