Okay kiddo, let's say you have a bunch of toys that you can group into different sets based on their colors. For example, you have red toys, blue toys, and green toys.
Now let's say your friend wants to play with some of your toys but they only like blue toys. You could go through and pick out all the blue toys for your friend, but that's a lot of work!
Instead, you can make a new set called the "blue toy set" and put all the blue toys in there. This is called a quotient set because you're taking the original set (all the toys) and dividing it up into smaller sets based on some criteria (color).
Now your friend can just ask for the blue toy set and they'll have all the toys they want without you having to go through and pick them out one by one. Pretty cool, right?