A private key is the way you access bitcoin. It's a string of numbers, and without it, you cannot access your "wallet". Think of it a bit like having a key to a security deposit box full of money, and if you lose the key there's no way to get a new one - the money's stuck in there forever. Typically people store these somewhere "safe" and offline, either written down somewhere or stored on a hard drive -
there's a man who keeps trying to dig up a landfill because his girlfriend accidentally threw out his hard drive.
If a lot of very wealthy people lose their bitcoin keys, then this significantly increases bitcoin scarcity, which will make the remaining bitcoin more valuable.