A medication's half-life is how long it takes for half of it to be eliminated from the bloodstream. In medical terms, the half-life of a drug is the time it takes for the plasma concentration of a drug to reach half of its original concentration.
One impact of half-life is found in the SSRI antidepressants. People taking SSRIs with short half-lives are much more likely to experience SSRI Discontinuation Syndrome. People taking an SSRI with a long half-life such as Prozac need to wait far longer between stopping Prozac and starting to take an MAOI antidepressant (see MAOI Antidepressants).
Interestingly, no matter what the half-life of a medication is, it takes about 4 times that half-life for the concentration of a medication in the system to reach a "steady state." This means that if you begin taking a medication with a half-life of 24 hours, after four days, or on the fifth day, the rate of intake of the drug will approximately equal the rate of elimination. If the half-life is 12 hours, you'll reach that state at the beginning of the third day (after 48 hours).