What do they mean by these numbers and letters such as t(8;21), t(15;17)
They refer to genetic (secondary chromosomal, specifically) abnormalities, actually. It is speculated that certain translocations (t) and inversions (inv) dramatically increase the long-term survival rate of patients with leukemia. Generally speaking (for experimental/analytical purposes), t(8;21) refers to the loss of a sex chromosome, t(15;17) to trisomy 8, and inv(16) to trisomies 8 or 22.
It's a branch of biology that deals with heredity, and cellular components (chromosomes in particular) associated with heredity.
The prefix cyto is derived from the Greek "kutos" (meaning 'hollow container') It or its cousin the suffix "-cyte" are used in biology to denote the cell. That gives us cell genetics. Or, more specifically, the science concerned with the study of (chromosomes as they relate to) cell division.
Should I ask his doctor if he has normal, good, or poor-rish cytogenetics?
If he was subject to one of the aberrations listed, he would already know about it, most likely, and so would his doctors. If they somehow didn't, they would've discovered it very quickly.
Point of clarification, though: in this case, "normal or good" cytogenetics are disadvantageous (only in this specific context, of course, the vast majority of the rest of the time they are most desirable). The abnormalities they refer to are maladaptive normally, but are suspected of being of benefit when endeavoring to survive leukemia.
Don't get all worried that your dad doesn't have any of them. If he did, he would very likely have died well before you were born. All 3 conditions are quite rare, with the possible exception of the first (which it is not possible for your dad to have - due to his being of the male sex). And remember, contrary to what that particular source claims, the odds are more like half. As of a while ago. We take great big strides and even make leaps on a daily basis.