Cats evolved to hunt for food. And given how many birds, chipmunks, bunnies, mice etc. outdoor cats catch (and sometimes bring back home) they haven’t lost those instincts. They also sometimes stalk us, thankfully that usually doesn’t result in any serious damage.
It isn’t uncommon, however, for our cats to become too sedentary and put on an unhealthy amount of weight. One way to encourage some activity is with puzzle feeders. These also let you reduce food while also giving some extra food they can get with more effort.
This webcast shows an example of a simple puzzle feeder you can make yourself. There are also many available for purchase including: Trixie Mad Scientist for Cats, Catit Design Senses Treat Maze and Egg Cersizer Interactive Toy and Food Dispenser.
Here is a home made version of one of those for sale above being used by a dog: