Have you ever played with a rubber band and stretched it with your fingers? Imagine that the rubber band is a string, and the way you stretch and twist it is like the movement and shape of the string in topological string theory!
Topological string theory is a way to study the behavior of strings (like the rubber band) in the context of topology, which is a branch of mathematics that deals with the properties of space and geometric shapes. In topological string theory, the properties of the string don't change, no matter how much you stretch or bend it.
Imagine drawing a string on a piece of paper, and then stretching it as much as you can without breaking it. The shape might change, but the overall structure of the string remains the same. This is the basic idea behind topological string theory.
Scientists use topological string theory to explore the behavior of strings in different dimensions, and to understand the geometry of space on a very small scale (much smaller than what we can see with our eyes). It has applications in physics, including in the study of black holes and the structure of the early universe.
So, in short, topological string theory is a way to look at the behavior of strings while focusing on their unchanging properties, even as they are stretched and deformed.