maybe bushes, but most likely dampers.

commonly known as shock absorbers, although the springs are actually the shock absorbers.
if you have just a spring, without a damper or with a knackered damper, the car will bounce a lot over a bump or due to weight transfer (like american cars in old movies where you see them stop and the front wobbles up and down for ages).

the damper has a piston that moves through oil, and it's difficult to move through the thick oil with only a small hole in it to allow it to move. that has the effect of letting the spring compress to absorb a bump, but then extend again slowly so that it doesn't keep bouncing.

to check it, you need to bounce each corner hard (maybe get a beefy man to help). as soon as you stop bouncing it, it should settle down and stop. if it does more than 1 bounce (maybe more for a softer family car), then they're knackered. and you should change them in pairs.

new dampers make a hell of a difference to handling, but aren't cheap, particularly front ones if you have to pay to have them fitted.