There is no "whole time". When you take a medicine, a certain portion of it gets into your blood stream and permeates your body. Immediately your liver and other body parts start deactivating and removing it. If the half life is 12 hours, then at 12 hours half of it is gone, so you are down to 50% of the peak level. In another 12 hours, you are down to 25%, then 12.5%, and after about 5 half lives, so little is left we consider it pretty much gone, but trace amounts actually remain in your body for longer.

It's also useful to know that if you keep taking the drug, let's say for a condition like epilepsy where you need a constant minimum amount of drug in the body, at first it starts to accumulate in your body as you are adding more drug before the previous dose is cleared, and it takes about 5 half lives before you reach a steady state or plateau, where the blood level is the same every day. It still shoots up to a peak after each dose, and then drops somewhat before the next dose, but the peaks and valleys are the same every day at steady state, so you can be confident that even at the lower blood level just before each dose, there's enough drug to prevent seizures.

Half life is also useful to know if you stop a drug, because you know that in about 5 half lives it'll be pretty much gone.

Sometimes half life can change due to some other drug or medical condition, and that is useful to know as it may mean you have to adjust the dose of your drug to correct for that. In overdoses, sometimes the mechanisms that clear drugs from the body can't scale up to deal with high drug levels, and the half life is longer and it takes longer than expected to recover.