A quasitopological space is like a place where we can play hide-and-seek.
You know how sometimes when you are playing hide-and-seek, you can hide behind something but still be seen? Well, in a quasitopological space, you can have something that is hidden but not really hidden. It's like a secret that is not really a secret because everyone knows about it.
Think about it this way: a topological space is like a playground where there are rules for how you can move and where you can go. But in a quasitopological space, those rules are a little bit more flexible. You can still play by the rules, but sometimes you can find a way around them.
So, a quasitopological space is like a playground where you can play hide-and-seek, but sometimes the thing you are hiding behind isn't really hiding you. It's a little bit sneaky, but it's still a lot of fun!