Covariance measures how much two variables, x and y, vary together. It is similar to correlation but the result does not get normalized to be between -1 and 1.
If x and y have a high covariance, then when x is large y is also large. When x is small then y is also small.
If x and y have a very negative covariance, then when x is large y is small. When x is small then y is large.
If x and y have a covariance close to 0, then changes in x do not correlate with changes in y. When x increases y does not always increase or decrease.
When To Use Covariance
Covariance is useful when you want to figure out if two variables change together. If two variables change together, then it might be possible to change one by changing the other.
If two variables have a covariance close to 0, then they are not likely related.
Regression can also be used to quantify the relationship between variables.