Groom can, of course, mean a few different things. You can groom a horse: brush it and clean it. A person can be groomed as well, if they look like they really take care of their physical appearance.
However, the one that interests us today is the sort of grooming one does in order to prepare you for something specific.
As in the example, you can groom you child to take over your business. You can groom someone to take the reigns of your talk show. So really, grooming here means teaching a person to do something a specific way in preparation for a particular role.
Can you think of any real life examples?