Whoever means any person at all, without specifying exactly who. When you say “Whoever left their backpack in the hallway should come get it,” you're talking to an unknown person. You don't know their name, but you know someone did it.

The word works like a blank that anyone could fill in. If a teacher announces “Whoever finishes first can help me set up for science,” she means any student who finishes first, not one particular person she has in mind. If your mom says “Whoever cleans their room first gets to pick the movie,” both you and your sister have the same chance.

Whoever appears often in rules and announcements because it applies fairly to everyone: “Whoever arrives late must get a hall pass” means the rule works the same way for any student. It also shows up when the specific person doesn't matter: “You can invite whoever you want to your birthday party.”

Notice that whoever is different from whomever, which sounds fancier and is used in some very formal writing. In everyday conversation, people almost always use whoever, and that's usually fine.