Cats are acting on their natural parenting instincts when they bring dead mice and birds home to their owners. In the wild, mother cats bring home their catches in order to feed their families. In a domestic situation, cats look to their owners as surrogate family members.
In addition to feeding their families, cats bring home dead mice and birds in order to teach their young how to hunt. These instincts work the same way with domesticated cats. Instead of teaching their young how to hunt, they try to pass their skills and knowledge on to their owners.
Another common theory is that cats bring home dead animals as a token of appreciation for their owners. According to "The Cat Behavior Answer Book" written by Arden Moore, hunting prey and bringing it home is a cat's way of showing love for their owners and their hunting instincts are deeply ingrained.
In addition to mice and birds, cats are also known to bring home insects such as cockroaches and crickets. Typically, domestic cats tend to leave their catches in the open for the owners to see, but it is also common for cats to bring their catches home and bury them in a safe hiding place. Cat owners can curb hunting behavior by placing bells on their cats' collars, as the ringing sound gives potential prey a chance to get away before the cats can pounce.