To groom means to take care of the appearance, whether it's plucking eyebrows or combing hair. When you spend over an hour grooming in the bathroom, combing your mustache and buffing your nails, you drive everyone else who needs to use the bathroom crazy.
You can groom something besides a person. Resorts groom their golf courses and ski runs. If you own a horse, you groom it every day. Animals groom each other by picking off insects and licking at fur. You can also use groom in regards to the mind. If you are being groomed for a certain spot or position, you are being prepared to take over its activities and responsibilities. Let's hope that you will someday be groomed for a spot on an executive board. And last but not least, the man getting married at a wedding is the groom.