To add a little to the above, Douglass says that when he first hears the phrase, he does not understand what it means. He hears it often, so he decides to use the dictionary to look up the phrase. The dictionary affords him little help and understanding, so he waits until he can read a newspaper for information. In the newspaper, he learns the meaning of abolition. He recalls the situations during which he has heard the phrase "the fruit of abolition," and indeed it refers to situations that proponents of slavery consider bad: slaves running away and succeeding in their efforts, slaves killing masters, setting fire to barns, or anything else considered "wrong" by the slaveholders. People regard the abolitionist movement as a source liberal ideas, one that gives slaves the notion that they can, and should, be free and that others in the movement believe in their right to be free.
I think that you are talking about a passage that can be found in Chapter VII of this book. In it, Douglass describes his confusion over the phrase that you mention.
Douglass says that he hears people use this phrase quite often. They use it when referring to anything that a slave has done "wrong" -- things like trying to escape or like burning down a barn. He does not understand what that means.
What it means is that the Southerners are blaming Northern abolitionists for all of these things. They say that the abolitionists put "bad" thoughts into slaves' minds. The abolitionist ideas stop the slaves from being content and make them do these "bad" things. Thus, the "bad" actions are caused by abolitionists.