Okay kiddo, so you know how some people use their phones more than their computers to look at stuff on the internet? Well, sometimes when people make websites, they only think about what it will look like on a computer screen. But that can make it really hard to use on a phone because everything is so small and hard to see.
So, a mobile-first design means that the people making the website think about it first on a phone and make sure it looks good and is easy to use on a phone. Then, they make it work on a computer screen too. That way, more people can use the website no matter what device they are using. It's like building a house - you start with the foundation (the phone version) and then build up from there (the computer version).