To clean an animal, often by brushing its fur. (Cambridge Dictionary)
A groom is someone whose job is to look after the horses in a stable and to keep them clean. (Collins Dictionary)
If you groom an animal, you clean its fur, usually by brushing it. (Collins Dictionary)
Brush and clean the coat of (a horse, dog, or other animal) (Oxford Dictionaries)
(of an animal) clean the fur or skin of (itself or another animal) (Oxford Dictionaries)
Give a neat and tidy appearance to (someone) (Oxford Dictionaries)
When did grooming became a dirty word?
Understanding Why Cats Groom Themselves.
Why do grooms carry brides over the threshold?