what does "heuristically" means? What does it mean when an author illustrates a result or proof of some result "heuristically" ? And why is that useful ?

Here is a very common example: We define the Riemann integral as sums of rectangles approximating the area under the curve, and then take the limit as the "width" of the rectangles go towards zero. This, along with the picture, is a more or less heuristic definition of the Riemann integral, in that the formalism is not in focus, but we concentrate on visualization and understanding.

Picture is from https://isquared.digital/blog/2020-05-27-riemann-integration/
