Imagine you wanted to play with a bunch of toys at a toy store. When you go in, someone gives you a box to put all the toys in. You can look at as many toys as you want and put them in the box, but when you leave the store, the box goes away.
A session in web analytics is kind of like that box. When you visit a website, the website gives you a new "box" called a session. Anything you do on the website, like clicking on links or typing in information, is put into that session.
Just like with the toy box, the website takes away the session when you leave the site. But before it does that, it looks at what you did during the session and saves it. This way, the website owners can see what parts of their website people are using the most, what people like about it, and what things might need to be improved.
So, a session is like a box that holds all of your actions on a website for a certain period of time, and web analytics use it to understand how people are using their website.