What is the scientific definition of half life?

Half-life ##(t_½)## is the time required for a quantity, or phenomenon to be reduced to half its initial value by whatever process is appropriate.
The term is very frequently found in nuclear physics, and indicates how quickly unstable atoms decay into other products, but in fact can be used to describe any type of decay process.
If you take a drug for example, it is possible to talk about how long it takes for half of that drug to be eliminated from your body.