This could any, or even all of these things -
- Worn universal joints in the steering column
- Worn steering rack
- Worn ball joints
- Loose steering rack mountings
They are all things you should be able to repair yourself.
While the car is stationary, get someone to wobble the steering wheel back and forth as far as it will move without the front wheels moving. Examine all of the components listed above to identify which component is allowing the movement.
If for example it is a universal joint on the steering column that is faulty, then you will see one side of the UV joint moving, while the other side is not. Likewise if the steering rack is faulty, you will see the input shaft moving back and forth, but the track rods going to the hub carriers will not be moving.
If you have to replace the steering rack or ball joints, then you will also need to get your wheel alignment adjusted.