The definition of marginal revenue product is the amount of change in revenue you get when you buy a unit of inputs.
The law of diminishing marginal returns tells us that as you add more inputs (short run) your marginal returns go down. This means that as you buy more inputs, you get fewer products in return for them.
If you are getting fewer products as you buy more inputs, that means you are also getting less money per input as you buy more inputs. This is why the MRP curve slopes downward.