The half-life of a nuclide is the length of time required for half of the nuclides in a sample to decay.
Imagine a table full of coins. On one side they are yellow and on the other side gray. At an initial time t0, they all show their yellow side. After one half-life (t1/2) we flip them all. Half of them will remain yellow side up, the other half gray. After another half-life we flip the yellow ones again, and half of those will also turn gray, leaving only 25% yellow remaining.
Let's imagine the yellow coins represent our nuclides, after each half-life, half of the remaining nuclides undergo radioactive decay events. After another half-life, half of the remaining nuclides also undergo decay events, leaving only 25%. This process continues, halving the remaining active nuclides each time until there are no remaining active nuclides left, and stable daughter nuclides have been reached.