For a radioactive material it is the time taken for the radioactive activity to decay/reduce to half its previous value (on average) Depending upon the material it can be less than a second/a few seconds to many thousands of years. It is a natural property of the material and it can't be changed. Radioactive decay continues until the material changes to lead (metal) as this is the first stable element in the decay chain. http://en.wikipedia.org/wiki/Half-life

Radioactive decay occurs when a nucleus of a radioactive atom decays ie it gives off some energy in the form of radiation (alpha, beta or gamma) creating a more stable nucleus. When this happens is a random event; you cannot predict when an individual nucleus will decay but this event also has fixed probability which means that at any time you can say what proportion of the nuclei in some radiative material will have decayed. The most usual way of describing this is the half-life which is the time taken for half the nuclei to undergo decay. As general rule the shorter the half-life the more radioactive an isotope is. Some extremely unstable nuclei of artificial isotopes have half-lives measured in seconds, others in billions of years. Note that the half-life only refers to single decay. For many isotopes the decay products themselves will undergo decay creating a chain leading to a fully stable isotope. The question is now, why do you need to know? If you are working with a radioactive substance you are subject to the Ionising Radiation regs and you are required to appoint competent advisers in the form a Radiation Protection Supervisor (RPS) and a Radiation Protection Adviser(RPA) both of whom would be able to explain this phenomenon.