I have a bike which is about a year old. I went to ride it yesterday and saw the back wheel wobbling.
Is it a major problem or a easy fix?
There are a few things that could be described as a 'wobbly' wheel.
Hold the rear wheel off the ground, grab the tire at the 12 o'clock and 9 o'clock (from the chain side of the bike), try to move the rim sideways. If the wheel feels like it is moving (wobbling) on the axle (other that rotating), the hub bearings are damaged or need adjusting. Your local bike repair store can tell you if they can repair the hub, or if a new wheel is required.
Hold the rear wheel off the ground, spin the wheel, watch the rim relative to the brake pads. If the rim looks like it is moving in and out relative to the pads (wobbling) as it spins, the rim is out of true. If it moves a few millimeters, it wont really affect the bike. Any more, or if the rim is hitting the brake pads, the rim needs to be trued. Again, your local bike repair store can fix that for you.
Lastly, the tire may have become uncentered on the rim. If the rim runs true but the tire does not, you can deflate the tire and push and pull it to re-seat the bead on the rim.
A possibility not already mentioned is a broken axle: I had the axle on my 25-year-old mountain bike break while riding and although I noticed the tire was wobbling, it wasn't until I got to my destination that I realized what had happened. The axle had snapped in the middle (inside the hub), but the bearings stayed in place becuse the seat and chainstays were essentially applying compression force to the axle. I'm sure the inside of the hub was damaged from the broken ends rubbing but I've never looked to be sure.