Singular point of an algebraic variety

Okay kiddo, so picture a big playground with lots of different shapes and structures on it. Some parts of the playground might have slides, others might have monkey bars, and some parts might just be flat ground.

In math, we call these shapes and structures "algebraic varieties," and they're made up of lots of different points.

But sometimes, there are points on the playground that don't fit into any of these shapes or structures. They're kind of like their own special point, and we call them "singular points."

Just like how you might have a toy or a piece of clothing that's unique, singular points are unique in the world of algebraic varieties. They don't fit neatly into any of the other shapes or structures.

So that's what a singular point is – it's like a special, one-of-a-kind point that stands out from all the others on the playground.