Have you ever counted how many apples you have? Let's say you have three apples. When you say, "I have three apples," you are using a quantifier. A quantifier is a word that tells you how many of something there is.
Now, let's say you want to say that your friend also has three apples. You could say, "My friend has three apples too." But, if you use quantifier raising, you could say, "There are three apples my friend has."
Quantifier raising is when you take a quantifier, like "three," and move it to the beginning of a sentence. This lets you make sentences in a different way.
It's kind of like playing with blocks. You can take one block and put it somewhere else to make a different shape. When you move the quantifier in a sentence, you are rearranging the words to make a different sentence shape.
So, quantifier raising is just a fancy way of moving words around in sentences. It helps us to express the same idea in a different way.