Yes Infinity is not a number, but an abstract concept. (it's not a function)
However infinity is really useful in mathematics and science in general.
In arithmetic, it doesn't make sense to divide a number by zero. ( Dividing something by nothing. Like can you divide apples amongst no children, eg.)
Division by zero is considered undefined and indeterminate.
However in complex mathematics and even in calculus, (if you take the limit of x/y and y approaches 0 from either left to right, graphically you'd view that x approaches infinity negatively/positively blah blah)
However in layman's terms, I would just say.
"Hey. Division is repetitive subtraction. For eg, if you wish to divide 8 by 2, keep subtracting 2 from 8 until you get, 0 or a number less than 2 (for whole numbers it would be 1). The number of times you subtract is your quotient, 2 is your divisor, 8 is your dividend and 0 or 1 is your remainder.
Now if you wish to divide a number by 0, you'd have to repetitively subtract a number with 0.
Now think about it, when you subtract nothing from something, you're still left with something. So constantly subtracting a number with 0, just gives you the number itself.
So if you ever wish to reach a number less than your divisor, you'd have to KEEP subtracting 0 from your number forever.
If you ever stop, that would be your infinity"
(Division by zero leading to infinity in non-complex terms. My take on it. )