The half-life of a radioactive material is the time it takes for its activity to fall to half of its starting value. The half-life tells us how long the material stays dangerous, so the hazard from a radioactive material depends on it.
A source with a short half-life has a high activity at the start, because many of its nuclei decay every second. This gives intense radiation. But the activity falls quickly, so the source is safe after a short time. This is why sources used in hospitals, such as tracers injected into patients, have short half-lives.
A source with a long half-life has an activity that falls very slowly. It stays hazardous for many years. Radioactive waste with a long half-life must be stored safely for thousands of years, and any contamination of the environment lasts a very long time.
A smoke detector shows the idea. Its source is americium-241, which emits alpha radiation and has a half-life of about 432 years. The activity stays almost constant for the whole life of the detector, and the alpha radiation is stopped by air and the casing, so the hazard is small.