HTTP 303 is like a grownup telling you that you need to go find something in another room. This happens when you ask for something from a website, but the website knows that the thing you want isn't in the place you asked for it. So instead, the website tells your computer to "go to this other place" where the thing you wanted actually is.
For example, let's say you're looking at a website that shows you pictures of animals, and you click on a link that says "show me pictures of cats." But the website already knows that the pictures of cats you want aren't in the same place you currently are on the website. Instead of just saying "sorry, there are no cat pictures here," the website sends your computer a message that says "try looking in this other place for cat pictures." This message is called an HTTP 303 response.
So, your computer follows the message and goes to the new place where the cat pictures actually are. And if you're lucky, you'll get to see lots of cute kitty pictures!