A population is a large set of objects of a similar nature – e.g. human beings, households, readings from a measurement device – which is of interest as a whole. A related concept is a sample , a subset of objects is drawn from a population.
An important broad class of problems in statistics is concerned with making some conclusions about a population as a whole, when you only have a random sample from this population.
In mathematical statistics, analytical tools are developed mainly for infinite populations. If the population at hand (that is usually finite) is many times larger than the sample, then the infinite population formal model is quite adequate.
A population is not necessarily real – it may be hypothetical or imaginary. For example, outcomes of an experiment , that is carried out infinitely, make a hypothetical population. The goal of inferential statistics is to make conclusions about such a hypothetical infinite population from a finite sample obtained by repetition of the experiment or measurement a finite number of times.
For example, tossing a coin infinitely gives rise to a hypothetical population consisting of “heads” and “tails”. If a coin has been tossed a finite number of times, say, 100, then one has at hand only 100 outcomes, say, 55 tails and 45 heads. These 100 head/tail values comprise a sample from the infinite imaginary population.