Can you explain why surface runoff or rain not absorbed by the soil occurs much more often in areas with soils with a high clay content.?

Clay soils can absorb water, but do so only slowly because they are very fine grained, and the spaces between the grains are very small. This is in contrast to sandy soils where the spaces are big and water penetrates easily. During periods of heavy rain you can quickly get standing water on the surface of clay soils, which soon leads to run-off.