Is covariance a measure of variability?
In terms of linear regression, covariance is not technically a measure of variation.
Covariance describes the relationship between two variables and how strong that association is. Does an increase in X lead to an increase in Y? If the answer is yes, then covariance is positive. If an increase in X leads to a decrease in Y, then covariance is negative.
Strictly speaking, covariance is not a measure of variability (interquartile range, standard deviation, and etc. are all used to describe variability). Instead, it is a measure of association because it tells you the association between two variables.