Definition
Sampling is the procedure by which a subset of individuals — the sample — is drawn from a larger population in order to learn something about that population without examining every member of it. The sample is the empirical handle we get; the population is the thing we actually want to know about. The validity of any statistical conclusion depends on how the bridge between the two was built.
There are many specific designs — simple random sampling, stratified sampling, cluster sampling, systematic sampling, convenience sampling — and each trades cost against representativeness in a different way. The choice of design is rarely neutral; it shapes which questions the resulting data can credibly answer.
Why it matters
How it works
Probability-based sampling gives every member of the population a known, non-zero chance of being included. Simple random sampling assigns equal probability to everyone; stratified sampling first divides the population into strata (age bands, regions, severity categories) and samples within each; cluster sampling picks intact groups (schools, postcode districts) rather than individuals, which is cheaper to administer but adds dependence between observations. The defining feature of these designs is that the selection mechanism is documented and the resulting estimator's behaviour can be derived mathematically.
Non-probability sampling — recruiting from whoever happens to be available, posting an online survey, asking interview subjects to nominate further subjects — sacrifices that mathematical machinery for speed and access. Useful inferences are still possible, but they require assumptions about how the recruited sample relates to the broader population, and those assumptions are usually unverifiable from the data alone. The honest move with a non-probability sample is to describe what was actually collected and to be explicit about the populations the data does and does not represent.