To find the variance of a sequence of numbers, find the average of all the numbers and subtract this from each number. If you see a pattern that starts negative then goes positive, the sequence starts small and grows. If all the sequence of variance are mostly negative with a spike of positives about 3/4 of the way through the sequence, something is happening 3/4 of the way through the sequence.
To compute the covariance of two processes, compute the variance for each and multiply the sequences point by point then take the average. This single number (the covariance) can tell you a lot about how the two processes are related. The absolute value of the covariance indicates how strongly the two processes are related.
If the covariance is zero, the processes are not linearly related. They could be related in some non-linear way (for example, one could be the square of the other). If the covariance is positive, the processes are related--when one increases the other increases. If the covariance is negative, the processes are inversely related--when one increases the other decreases.