Covariance
A measure of whether two variables tend to be above or below their means at the same time.
Covariance is . When both variables are above their means together the product is positive; when they move oppositely it is negative; averaging those products says which tendency wins. Note that a variable's covariance with itself is exactly its variance.
The catch is that it has no fixed scale. Its magnitude depends entirely on the units involved, so measuring a length in metres rather than millimetres changes the covariance by a factor of a thousand while the relationship is unchanged. A covariance of 4.2 therefore means nothing on its own — divide by both standard deviations to get a correlation coefficient, which is bounded and interpretable.
Collecting the pairwise covariances of many features gives a covariance matrix, which is symmetric, has the variances down its diagonal, and is the object PCA decomposes.