The rule of succession is like when you play a game with your friends and you have to decide who gets a turn next. It's also used for when important leaders, like kings or queens, need someone to take their place when they can't do their job anymore, like when they get sick or die.
In a game, you might have a set of rules that say who goes next. Maybe it's the person who won the last round, or the person with the shortest hair. With the rule of succession, there are similar rules that decide who gets to be the next leader of a country or organization.
These rules are usually written down in something called a "constitution" or "charter." They might say things like "The oldest child of the current ruler will become the new ruler when the current ruler can no longer do the job." Or they might say, "A group of people will vote on who should become the new leader."
The rule of succession is important because it helps make sure that there is always someone in charge, even if the current leader can't do the job anymore. This helps keep things running smoothly and prevents chaos.