Analysis of covariance is a way of comparing two or more groups of numbers when some of the numbers might be related. It takes into account a measure called "covariate" that is related to all the sets of numbers. The goal of analysis of covariance is to tell us how different or similar the groups of numbers are, even when the covariate might be messing with the results.
To explain with an example: imagine you have two groups of people. Group A are teenagers and group B are adults. You want to compare how tall they are on average. But the average height of teenage group might be lower because they are all still growing. By taking into account the age (which is the covariate in this case), you can get an accurate comparison of the average heights of these two groups. Analysis of covariance is the tool used to figure out how much the age is affecting the results and make sure the comparison of the two groups is fair.