An index is like a big list or catalog of everything that a search engine has found on the internet! Just like how you might make a list of all your toys or books, a search engine like Google makes a list of all the web pages, videos, pictures, and other things it finds on websites.
Whenever you type something into the search engine, like "funny cat videos," it looks through this big list, or index, to find all the things that match what you're looking for. It can do this really quickly because it has organized everything in the list so that it's easy to find. Just like how you might alphabetize your list of books, the search engine sorts everything in the index by keywords or topics to make it easier to find.
So, when you type in your search, the search engine quickly looks through the index to find all the web pages and other things that talk about "funny cat videos." It then uses a special formula called an algorithm to pick out the best matches and show them to you in order of relevance!