The production function says how much output is produced when specific amounts of each factor of production are being used. One may draw up a long list of a country's factors of production:

the number of factories,
the number of workers, their qualifications,
the area and quality of land,
the climate,
natural resources,
the political and legal system, and so on.

It is useful to subsume the more important of these factors into either of two categories: capital K or labour L. So output Y at any point in time is a function of two factors only.

The relationship may be represented in a 3-dimensional graph. The full scale 3D production function shows how, for given production technology, output rises as higher and higher quantities of capital and/or labour are being employed.

Further reading on pp. 138-143.