How do the agriculture affect the accelerating growth of human population?

When fewer people starve to death each winter, and there's enough food for children to grow up to adulthood, then the population will naturally increase.

Without Birth Control, the average woman will have four or five children. Before modern farming methods (and modern medicine!) were developed, two of those children would die of starvation or disease. Improved agriculture enabled farmers to produce more food than they needed; the extra food could be sold, allowing people like artisans, blacksmiths, traders, Accountants, soldiers and sailors, nobles and kings to eat. The builders and carpenters and engineers improved society, but only because they didn't each have to grow their own food!