The Law of D.M.R. is an empirical law in economics

Many students often don't bear in their minds of the importance of the following law:
the Law of Diminishing Marginal Returns ----
A principle stating that as more and more of a variable input is combined with a fixed input in short-run production, the marginal product of the variable input eventually declines.
It is a very important economic principle underlying the analysis of short-run production for a firm. It offers an explanation for the upward-sloping market supply curve.

How does the law of diminishing marginal returns help us understand supply? The law of supply and the upward-sloping supply curve indicate that a firm needs to receive higher prices to produce and sell larger amount quantities of the good or service concerned. Why do they need higher prices?