This is an very basic introduction to the ideas behind calculus. I normally do this investigation a year before we start with proper calculus.
It is based on the idea that the gradient of a line (tangent) going through the point A on a curve will be somewhere between the gradient of line AB and AC if B and C are also points on the curve.
But the closer B and C is to the point A the smaller the interval will be and the better you will be able to estimate the gradient of A.
This leads learners to the idea that if the distance between A and B is zero they will be able to calculate the gradient in A. But that is impossible, hence the need for limits.