An ad hoc explanation is an unfalsifiable explanation provided in an effort to account for an inconsistency in a theory.
For example: A child says that he turned his homework in to the teacher. The teacher then confronts him with the fact that the homework is not in the box. The child responds, "Somebody must have stolen it!" The child has no evidence to support the allegation that someone stole the homework -- he has simply manufactured an unfalsifiable explanation to deal with a difficulty in his story.
Ad hoc explanations commonly appear to prop up poor theories in the sciences. For example, the ptolemaic system, which held that all heavenly bodies moved in concentric spheres around the Earth, faced continual difficulties from new and unusual observations -- notably the planets, which did not move with the other stars. In order to deal with these difficulties, increasingly complex and arbitrary alterations to the scheme were added. The ad hoc solutions were able to make preferred theory match observed facts, just as "somebody stole my homework" explains the gap between the child's claim that he turned in his homework and the fact that it isn't there. However, over millennium, the addition of more and more ad hoc explanations made the model seem less and less reasonable.