"Half life" is a scientific term. It means the length of time it takes for 50% (half) of a substance to disappear/decay/be used up. Its a term commonly used in either drugs, or radioactive substances. With drugs, some have a very short half life, which means that the effects only last a matter of hours then its completely used up by your body. Other things stick around in your body for a lot longer, even though you may have to keep "topping up" the dose to keep it in the therapeutic range, i.e. at the level that it feels like and is doing something.
