Okay kiddo, let's talk about something called "vanishing at infinity." Have you ever seen a road that goes on and on and seems to disappear in the distance? Well, in math we also have something like that, it's called infinity.
When we say something vanishes at infinity, we mean that as we move further and further away from a starting point, that thing gets smaller and smaller until it's almost gone. For example, let's say we have a big piece of cake. If we start taking small bites out of it, eventually the cake will be all gone. Similarly, if we have a function in math, and we keep plugging in larger and larger numbers, sometimes the answer gets smaller and smaller until it's almost zero. That's what we mean by vanishing at infinity.
So next time you see a road disappear into the distance, remember that it's like infinity in math, and things can vanish into nothingness as we move further away from them.