The brief story about Franklin's neighbor from page 88-89 of his autobiography can be summarized with the quote "Yes, but I think I like a speckled axe best." Franklin brings up the story in the context of his 'Order' virtue. His neighbor, when buying an axe from a local smith, said that he wanted the whole axe to be bright like the edge. When he and the smith set to actually polishing and grinding the whole axe, the neighbor quickly became tired and gave up after the axe was only speckled. The obvious point of the quote is that some goals take too much work to accomplish to be worthwhile (that is, that sometimes you have to make compromises with yourself and that you won't always get what you want). This relates to Franklin's overall view of his self-examination, in that it benefited his life in the long run even though he wasn't able to maintain any kind of focus on the virtues for a long period of time.
The quote itself actually goes beyond this idea, because if it was just about the benefits of compromise, it would read something more like "I think a speckled axe is fine." By saying that the speckled axe is actually "best," Franklin's neighbor is saying (even if he didn't mean it) that, even if the axe was perfectly shined, the half-grinded speckled axe would be better. Franklin goes on the elaborate on this, saying that being perfectly moral would bring about new problems and difficulties in personal relations. His message is that sometimes being the best isn't necessarily that much better than just being good, whether you're talking about being virtuous or any other aspect of one's life.