A four beat canter is when the diagonal pair that usually hit the ground together are out of sync. It is not a "true" canter as the footfalls are not correct. It can be caused by a horse that is not forward enough, or is trying to break gait to a trot, or it can also be caused by pain and lameness.
There was a lot of this with the ultra slow western lope in the show ring. Conformation can have a bearing on whether or not the horse is capable of doing a slow 3 beat canter. Instead these horses will 4 beat. The ultra slow canter had to have been the dumbest, most inane gait for a quarter horse that was bred to be a sprinter.
It's when the front end and the back end are not "in sync" with each other, either out of laziness, poor training, lack of balance, lack of cadence, lack of topline/muscle, pain, fear, etc.
It usually feels disjointed, hind of like a herky-jerky motion in your hips, or it feels like your horse is divided with the front doing one thing and the back doing another. A true collected, cadenced, three beat canter is much more comfortable to ride.
In addition to above, a true canter is 3 beat. Anything out of that is not something you want.
Most commonly you'll see a 4 beat canter when the horse is not ridden forward and is on the forehand. In Dressage, you often see if where the horse is ridden front to back, or has been forced into a greater degree of collection in the canter than he is ready for.
Some horses will naturally have a 4 beat canter, if you want a trail horse it is quite comfortable to sit on when the horse is naturally in balance while 4 beating, but in looking for a competition horse you would run a mile in the other direction.
You can make a trot, but a walk and canter need to be naturally good.
Then of course you have the physical issues also which may be the cause of the incorrect canter.
It's something that only the most accomplished riders can achieve and only with the most talented of horses can this be done (that was a funny haha)
As said above, a four-beat canter is an incorrect canter that is either caused by pain or incorrect training. Western pleasure horses are built to move a specific way but they can't all move at that insanely slow pace like the ones that almost look like they are halting a moment before each stride. When a person takes a horse that is built to lope at a comfortable but slightly faster pace and forces them to match the speed of that horse ridden by the trainer that wins every class they end up with the broken four beat gait.
Question: What is the gait on a gaited horse? Is it two?