Half-life is the time it takes for the concentration of a drug in the blood to drop to half its previous value. It is a useful shorthand for how long a medicine lingers, and roughly four to five half-lives are needed for most of a dose to clear.
Half-life is not the same as duration of effect. A medicine can stop producing a noticeable effect while measurable amounts remain, and residual amounts can still contribute to next-day grogginess. Published half-life values are population averages and vary with age, liver function, kidney function, and other medicines.