A mare is an adult female horse. If your new horse is a filly, a female baby horse, she'll grow up to be a mare.
Horse experts have many words to distinguish the age and sex of their animals, from foal, for any newborn horse, to stallion, a full grown male, to colt, a young male horse. Mares are known for being more easy-going than stallions, and because they're equally fast and powerful, they're as likely as males to be used for racing. Another meaning of mare ("sea" in Latin) is "dark areas of the moon," once believed to be actual oceans.