A suspensory is like a smallish jock, which is meant to contain the balls only --- there is an opening for your penis to pass through.
A websearch will show you.
You might wear it if you have a hernia or a risk of one, but some guys might benefit from wearing one if they have very large testes. I qualify on that account, and a friend sent me one to try (it seems some of them come in a range of sizes). But I discovered that in my case supporting the balls only was not enough.