half-life
Imagine you start with a full jar of something that is being used up. The half-life is the time it takes for exactly half of it to be gone. Then in the next half-life, half of what remains disappears, and so on — a familiar rhythm if you have ever heard how radioactive substances 'decay by half' every so many years.
In kinetics, the half-life of a reaction is the time required for a reactant's concentration to fall to half its current value. Its behaviour depends sharply on the order of the reaction: for a first-order reaction the half-life is the same no matter how much you start with, which is its hallmark; for a second-order reaction the half-life lengthens as the reactant runs low; for a zero-order reaction it shrinks. So measuring how half-life changes is itself a way to diagnose the order.
Half-life matters because it is an intuitive, concentration-free way to talk about timescales — how long a drug stays effective, how long a radioactive sample remains hazardous, how long a stored chemical lasts. The caveat is that constant half-life is special to first order; for other orders you must say at what starting concentration the half-life was measured, or the number is ambiguous.
Carbon-14 decays with a half-life of about 5730 years. Start with 100 grams and after one half-life roughly 50 remain, after two about 25, after three about 12.5 — the same span of years halves the amount each time, which is the signature of a first-order process.
Constant halving time is the fingerprint of first-order kinetics.
Only for first-order reactions (and radioactive decay) is the half-life independent of starting amount. Assuming this for every reaction is a frequent mistake.