When you want to play with your favorite toys, you usually go to a friend's house because they have them. In the same way, when a website or application wants to play, they go to someone else's house to store and run their stuff.
This someone else is a Hosted Service Provider. They have big computers called servers that can store lots of websites and applications for lots of people. They keep these servers in a safe and clean place called a data center.
Using a Hosted Service Provider is like renting a room in a hotel instead of owning a house. You pay them some money, and they take care of everything, like keeping the servers running, making sure they are secure, and backing up your stuff.
This way, you don't need to worry about any of that, and you can focus on making your website or application work the way you want it to.