An explanation is a statement about how or why something is the way it is. If you're failing math, you'd better come up with a good explanation to give to your parents.
Explanation is from the same Latin word as explain: explanare, which means make clear. Because explanation and explain are so closely related, people often try to shoehorn an extra i into the spelling of explanation. Don't. You might think that explanation has the odd spelling, but it is really the more regular of the two because there is no i in explanare.