In this sentence, the connotative meaning of the word "heart" is the deepest part of Douglass' being (B).
The connotative meaning of a word is what is suggested or implied by this word. It means that you shouldn't take the word literally. Often, it is its second or third definition in the dictionary, but it can also be a metaphor.
In this case, the connotation is used as an image for Douglass' core feelings and thoughts. In the excerpt, he is saying that the words he read or heard "sank deep into [his] heart," meaning that they touched him deeply.