A groom is the person who cares for horses at a stable. His duties include activities such as feeding, cleaning and perhaps exercising the horse. The groom is also responsible for keeping an eye on the health and welfare of the horse, and will likely be the one to administer drugs or care for wounds and swellings. Other duties may include cleaning and caring for tack, keeping the tack room organized, the feed shed rat free and the stable neat and tidy.
A groom may also be required to help out at competitions. If so, they may be responsible for making sure the rider knows when their events are, which rings, and then making sure the horse is ready to go. At a dressage competition they may be required to call out the test if the rider hasn't memorized it, while at jumping events the groom will be needed to fiddle with warm up fences. At eventing competitions, their main duty will be keeping the horse sound and healthy, and making sure the rider isn't too stressed out.
At competitions it is often a rule that only one person may ride a horse on the grounds, and thus the groom will not be able to warm up the horse. Sometimes the groom is not an official employee; very often teenagers are conned into extremely hard work, with a horse to ride as their payment.
A groom is also sometimes called a strapper.