We've all been there: our wonderful furry friend brings a dead mouse/bird/chipmunk/bug/lizard/other critter and leaves it for us to find. Or, worse, gives it to us alive. As humans, we find it disgusting, but to the cat, it's a gift!
Why do our cats bring us "gifts"? Answer: they think we're incompetent.
Okay, not really. Cats bring gifts of food to us because they think of us as really big cats. They want to take care of us by bringing us food--and they expect us to be impressed by their hunting prowess. In the wild, cats bring food to their family and friends. They show respect and caring by sharing their kill. Mother cats bring food to their kittens. Cats may bring food to another cat who is injured or otherwise unable to hunt for itself. Our cats bringing gifts is a sign that they think of us as one of them. That's a pretty big honor!
Of course, that sign may be that they see us as kittens (or feeble cats) who are unable to provide for themselves, but I prefer to think that they're showing love and affection. We should make sure they know we appreciate the gesture. Even if it grosses us out.
Sometimes--if we're lucky--our cats will leave "dead" toys instead of the real thing. I often find mousies in my bed (and sometimes the bathtub, but I'm not sure if there's a message in that). Hide and Seek are trying to show me that they love me. Or that they feel sorry for me for my lack of hunting skills. Whichever.