Why scientists care
Half-life is the time required for the expected number of undecayed nuclei, or equivalently the activity of a large sample, to fall to one half of its initial value.
Successive half-lives produce halves, quarters, eighths and so on; the process is exponential rather than linear.
A concrete example
A half-life does not mean every nucleus survives exactly that long; it is a statistical property of a population.
Try to notice
Science becomes memorable when a definition is connected to something measurable or observable.