Fruitless things are futile or pointless. If your search for your missing car keys is fruitless, you don't find them no matter how hard you look.
You can call a fruitless search a wild goose chase — despite your efforts, you're unsuccessful. If you spend a fruitless afternoon applying for jobs, you end up without a single offer, and if your attempt to get your dog and cat to be pals is fruitless, they end up hating each other just as much as they ever did. The adjective fruitless comes from the sense of "unproductive" or "without profit," like a fruit tree that doesn't grow any fruit.