Usually: A loose exhaust heat shield, which rusts at the edges and vibrates.
But it can also be: Loose exhaust mounts, or something in the car itself — a jack, a bottle, a loose trim panel.
Rattling over bumps
If your car makes a tinny rattling noise every time you go over a bump, the most common cause is a heat shield. These are thin metal panels wrapped around parts of the exhaust to keep heat away from the plastic and rubber underneath. They rust at the edges over time, and once the metal thins out, they lose their stiffness and buzz against the exhaust pipe or the underbody whenever the car flexes over uneven road.
Here is a simple way to tell if that is what you are hearing. If the rattle changes when you rev the engine in park — not just when you hit a bump — that is a strong sign it is a heat shield. The vibration from the engine itself is enough to set a loose shield buzzing, separate from anything the suspension is doing. A loose exhaust mount, by contrast, tends to show up more as a clunk or a knock when you go over bumps, and less as a rattle when you simply rev the engine standing still.
It is also worth ruling out the cheap explanation first. Pop the trunk and check for anything loose in there — a jack, a tire iron, an empty bottle rolling around. Same with the glovebox and door pockets. It sounds obvious, but we see it often enough that it is worth two minutes before you assume it is something under the car.
As for whether it is safe to keep driving: in almost all cases, yes. A loose heat shield is annoying, not dangerous. It will not affect how the car handles or stops. The exception is if a shield has actually broken loose and is hanging down low enough to drag on the ground or catch on something, which is rare but worth a quick look under the front and middle of the car if you can.
Fixing a heat shield is usually straightforward. Sometimes it just needs to be re-clipped or bent back into position. If the metal has rusted through, the shield itself may need to be replaced or, less often, removed if it is too far gone to reattach safely. It is not a big job, and it does not need to be urgent. If it turns out to be a loose exhaust mount instead, that is also a routine repair — a new rubber mount, nothing more involved than that. Either way, it is a good one to mention next time you are in for an oil change rather than something to lose sleep over.