A "wobbler" is a horse with a deformed cervical (neck) vertebrae that presses on the spinal cord. It's seen in young horses as they grow and is most common in Thoroughbreds, because of their long spine and rapid growth pattern. It is twice as common in males as females.
They're called "wobblers" because they are clumsy and uncoordinated. The actual root cause is difficulty knowing where their feet are (some normal horses may appear this way, coordination does vary).
Wobbler syndrome can also be caused by arthritis of the spine in older horses.
Some foals with wobbler syndrome recover if they are put on a diet to slow their growth, although many growing horses have their clumsy phases anyway, so it can be hard to tell.
Wobbler syndrome often needs to be treated surgically, by fusing the affected joint with a metal insert. This has about a 75% success rate, but even with surgery some wobblers are never anything but pets. - and some vets recommend that horses with the syndrome never be ridden.
Fortunately, not all clumsy horses have wobbler syndrome. Many just can't be bothered to pick their feet up.