In an exponential decaying system, the time taken for the quantity or activity of a substance to halve. It most commonly applies to drug metabolism in a biological system, but equally applies to radioactivity of radio-isotopes.
The concept of a half-life of a drug within the body is often more complex than in a physical system as the effective activity of a drug may be reduced by several, often co-existing, mechanisms, e.g. re-distribution, excretion and metabolism. Furthermore, these factors are subject to intra- and inter-individual variation. Furthermore, metabolism of drugs may result in by-products that may have even more biological activity than the parent compound, prolonging the 'effective' half-life.
For clarity, if referring to a particular aspect of drug metabolism, the half-life can qualified, by referring, for instance, to elimination half-life.
In the absence of loading dose, 4-5 times the half-life (subject to the caveats above) can be used as an estimate of how long it takes to achieve steady-state.