Question

What are variance and covariance? What do they mean? What are their differences/relationship?

Answer 1

Variance is a measure of dispersion of a single random variable X. Covariance is a measure of how much TWO random variables, say X and Y, change together. (The variance is a special case of the covariance when the two variables are identical.)

Answer 2

If you remove the word "random", I would agree with your descriptions of variance and covariance.

Answer 3

A "random variable" is a technical term: it does not mean a variable that is "random" in the colloquial sense. The definitions above are taken from the "variance" and "covariance" entries in Wikipedia, but can be verified at any site containing a statistical glossary, e.g. netmba.