Ionising radiation can damage or kill living cells, and it can cause mutations in DNA that may lead to cancer. How dangerous a source is depends on the type of radiation, the dose a person receives and the half-life of the isotope. The half-life is the time taken for the activity of a source to fall to half of its starting value.
A source with a long half-life stays dangerous for a long time, because its activity falls very slowly. Radioactive waste of this kind must be sealed in shielded containers and buried deep underground, and then monitored for thousands of years. If it escaped into the environment, it would be a hazard for generations.
A source with a short half-life has a high activity at first, because many nuclei decay each second, so it gives a large dose in a short time. It needs care while it is active, such as thick shielding, tongs and short handling times. But its activity falls quickly, so it becomes safe after a short time, and the waste can be stored until it has decayed. For example, a tracer with a half-life of 6 hours has had 12 hours, which is two half-lives, so the activity has fallen to one quarter of its starting value. Each further half-life halves the activity again, so after three half-lives it is one eighth.
If two sources contain the same number of nuclei, the one with the shorter half-life has the higher activity at the start, but its activity falls faster, so it becomes safe sooner.