Okay kiddo, so you know how sometimes kings and queens have babies and those babies may become the next king or queen when the old one is no longer able to do the job? Well, the Royal Succession Act 2013 is a set of rules that says who can become the next monarch of the United Kingdom.
Before this law was made, the oldest son of the current king or queen would always become the next monarch, even if he had older sisters. But now, the oldest child (whether a boy or a girl) will become the next monarch, and it doesn't matter if they have older siblings who are boys.
Also, if the monarch wants to marry someone who is Catholic, they can now do that without giving up their position as monarch. This is because before this law was made, the monarch had to be a member of the Church of England, which is Protestant.
So basically, the Royal Succession Act 2013 is a set of rules that make sure the next king or queen is chosen in a fair way, and it also makes some changes to the old rules so that they are more modern and inclusive.