The production function is defined as the relationship between inputs used and output produced by a firm. For various quantities of inputs used, it gives the maximum quantity of output that can be produced. It establishes an exact relation where for any specific level of inputs, there is only one corresponding level of maximum output.

This function deals only with the efficient use of inputs, implying that it is impossible to obtain more output from the same level of inputs. It is defined for a given technology, meaning the technological knowledge determines the maximum output levels. If technology improves, the obtainable output increases, creating a new production function.

It is mathematically expressed as $q = f(L, K)$, where $q$ is the maximum output, $L$ is labour, and $K$ is capital. For example, for a farmer producing wheat, it shows the maximum output possible for a given amount of land and labour hours.