Correlation
Correlation is a pattern in which two measured variables change together; it shows a relationship but does not by itself prove cause.
Definition
A correlation means two things tend to change together: when one goes up, the other goes up too, or goes down in a steady way. It is positive when both variables rise together, negative when one falls as the other rises, and absent when a scatter plot shows no pattern; a correlation found in observational data suggests a possible cause, but only a controlled experiment can test whether one variable actually causes the change in the other. Formally, the strength and direction of a linear association is summarized by a coefficient $r$ between $-1$ and $1$. A correlation can arise from direct causation, reverse causation, a confounding variable that drives both, or chance in a small sample, so establishing causation requires manipulating the independent variable under controlled conditions.
Example
Plants that got more hours of sunlight grew taller, a correlation between sunlight and height. Timing salt dissolving at $10^\circ\text{C}$, $30^\circ\text{C}$, and $50^\circ\text{C}$ gives $48\ \text{s}$, $26\ \text{s}$, and $14\ \text{s}$, a strong negative correlation between temperature and dissolving time; because temperature was deliberately set and everything else held constant, this one supports a causal claim. Across 20 rock samples, mass and displaced volume give $r \approx 0.99$ along a line through the origin with slope $2.7\ \text{g/cm}^3$, and here the correlation reflects a physical law (density is constant for one material) while the near-zero intercept is evidence that the measurements carry no fixed offset error.
Key Insight
Two things changing together does not always mean one causes the other: ice cream sales and sunburns both rise in summer, but ice cream does not cause sunburn. A third factor, or coincidence, can make two variables move together, which is why scientists design experiments instead of only looking for patterns. A high $r$ says the points lie near a line and nothing more; it does not say the line is the right model, that the relationship is causal, or that it holds outside the range you measured.