A population is the complete set of individuals, items, or observations that a statistical study aims to describe. The population is what we want to know about; a sample is the subset we actually observe. The population may be finite (all students in a school) or conceptually infinite (all possible rolls of a die).
Population parameters — the mean, variance, proportions, and other summaries of the full population — are typically unknown and must be estimated from sample data. The goal of statistical inference is to draw conclusions about population parameters using sample statistics, together with a measure of uncertainty (confidence intervals, p-values, or posterior distributions).
A well-defined population requires clear membership criteria: who or what is included, and who or what is excluded. Ambiguity about the population leads to ambiguity about what the statistical conclusions mean. The relationship between population and sample is formalized through probability theory: each sample is modeled as a random draw from the population, and the independence assumption justifies the mathematical machinery of inference.