Execution methods are ways to legally put someone to death. It's like when you play a game and you have to choose which way you want to win - either by shooting a target, throwing a ball into a hoop, or jumping over an obstacle.
When people do really bad things like hurt other people or kill them, the government can decide to use an execution method to punish them. Some countries have different execution methods, but some common ones include things like lethal injection, electrocution, or hanging.
Lethal injection is when someone gets medicine injected into their body that makes them go to sleep and then stop breathing. It's like how you might take medicine when you have a cold, but this is a really strong medicine that can stop your heart from beating.
Electrocution is when someone gets strapped down to a special chair and then they put a helmet on that has wires attached to it. Then they send electricity through the wires and it goes through the person's body. This usually causes their heart to stop beating.
Hanging is when someone gets a rope tied around their neck and then they get dropped from a high place like a gallows. This also causes their neck to break or makes them suffocate (which means they can't breathe).
While these might sound like scary things, it's important to remember that they are only used in rare cases where someone has done something really wrong and the government has decided it's the appropriate punishment.