Gaiters protect the sliding parts of the front suspension from dirt and water.
They are used at both ends of driveshafts, protecting constant-velocity joints from the ingress of dirt, and retaining the grease.
They also prevent the ingress of dirt where one component slides within another, for example, on suspension struts or the ends of steering racks.
Finally, they are also usually used to perform the same function on ball joints, which appear on suspension wishbones and steering tie rod ends.
The gear stick gaiter is to resist dirt entering the ball joint at the bottom of the stick and to not have oil or grease from the joint exposed to passengers.