Why does getting more output from each additional worker translate into lower costs for each additional unit of output?

The question makes an assumption that getting more output from additional workers, or in other words, increase in manpower, always results in lower cost for additional output,. This assumption is not always true. There are several component costs of the total cost. These include among others labour, material and equipment usage cost. There is no guarantee that sum of these unit production costs for these inputs for additional production achieved from additional workers will be less than the average unit cost of existing production. As a matter of fact even the average unit cost of labour need not be lower.

It will be reasonable to assume that additional production from additional workers will result in lower unit cost for additional production, only when we assume that the production facility has a fixed cost and is currently producing below the maximum production capacity. In this case the unit cost of additional production is lower because the fixed cost gets divided over larger number of units produced.

It should be noted that it is possible that unit variable cost may increase with production, and in this way offset the benefits of apportioning fixed costs over a larger production quantity.