In the short run at least one factor of production is fixed, a firm cannot change its scale of output in the short run. In the short run if a firm wants to produce more it must shift it's supply and use up more of its limited factors of production, so the firm increases a variable factor of production such as labour, to fixed factors of production like land and capital.
In theory when they increase the number of workers, marginal product will at first rise due to benefits that arise from SPECIALISATION and the DIVISION OF LABOUR, this means that each worker you employ will increase total output to more than the previous one. After a while marginal product (the gain in product for every new worker you employ) will start to decrease until the point in which it becomes negative, this is when the law of diminishing returns kicks in.
Basically each new worker you are employing once the law of diminishing returns kicks in will produce less than the last, this can be explained by things like a lack of capital equipment avaliable for the amount of workers, hence the term 'too many cooks spoil the broth.'
It can be shown by the average cost diagram, the shape of the average variable or marginal cost curves explain it, as the curves start to go upwards, this is the increase in costs from employing more workers matched with the lower marginal product each new worker has.