A wobble in the steering wheel feels like the wheel is shaking to the left and right. This may get worse the faster you are driving. Almost feels like the wheel has a mind of its own. If severe enough, then it may feel like like it wants to jump right out of your had.
There are several things that can cause this. Most common is a problem in one of the front tires. One may have a lump in it, or an irregular wear pattern. This is easy to feel. Just rub your hand along the circumference of the tires to feel for a lump, feathering, or roughness. A best rim can do this as well. Rotating tires is a good way to diagnose this. Out of balance wheel/tire may enhance the situation.
All tires in the last few decades are steel belted. If a belt has shifted, this would also cause the problem. This type of tire problem is a little harder to find. It is not usually visible. Swapping the front tires with the rear, then going for a drive would make the feeling change. Since now the tire with a problem is in the rear. This is assuming the rear tires that are now on the front are in good shape.
Loose steering components are another common cause. Inner or outer tied rod ends that are loose will make the wobble or shaking. These need to be inspected regularly. If one were to break, you would loose the ability to steer the car or truck.
Worn upper or lower ball joints, or other suspension parts is another possibility, along with worn control arm bushings.
Basically if your vehicle has this condition, get it checked as soon as possible by a mechanic, just in case it is a safety issue with a component that is ready to break.