Imagine you are playing with your toys and the person who is supposed to be in charge of your game (let's call them the "leader") is not doing a very good job. Maybe they are being bossy or not listening to everyone who wants to play. Everyone in the game starts to feel like the leader is not doing a good job and they want someone else to take charge.
A leadership spill is when that happens in real life, but instead of toys it's important grown-up stuff like running a whole country or political party. Just like in your game, the people who are not happy with the leader get together and decide they want to make a change. They hold a vote to see if they can find someone else who will do a better job of leading.
Sometimes, the leader who was voted out gets really upset and maybe even tries to stay in charge anyway. But just like in your game, the other people tell them it's not fair and that everyone needs to respect the rules.
So, a leadership spill is basically a big game where grown-ups get together and vote to see if they want someone else to be in charge because they don't think the current leader is doing a good job.