In addition, the downed trees have names engraved on them that Tom recognizes.  These people he remembers as being "wealthy and important" to society in the past, and should have been his first clue not to deal with the Devil, ie black man.  His sense of logic is overruled by his sense of greed and ambition. 

On that note, it will benefit you to remember that society and reason/logic are two of the classic elements that the Romantics were rebelling against.  They much preferred the individual to society as a whole and emotion/imagination to logic and reason. 

The names carved into the trees represent those who've sold their souls to the devil.  Tom doesn't notice the names on the trees until the black man begins telling him that the land Tom is on belongs to the black man.  Also, as proof that Deacon Peabody, the one who Tom believed to be the owner of the land, is not doing well, the black man points to a tree that is large and flourishing at the outer areas, but is rotten at the core.  On this tree was written the name, "Deacon Peabody".  The black man tells Tom, "Deacon Peabody be d--d...as I flatter myself he will be, if he does not look more to his own sins and less to those of his neighbors."  The reader shortly discovers that the identity of the black man is the devil.  Furthermore, the black man indicates that as he takes each soul, he cuts down the tree with that man's name on it.  He tells Tom that he'll have lots of firewood for the winter.

What do the trees symbolize in "The Devil and Tom Walker"?

The devil, otherwise known as Old Scratch, is taking Tom Walker on a guided tour of some trees in the forest. There are two remarkable things about these trees. First of all, although they seem healthy on the surface, in actual fact they're rotten to the core. Secondly, they all have the names of men carved into them, men like Deacon Peabody and Absalom Crowninshield. The implication is that these men are condemned to hell if they don't change their ways.

Here, the devil is giving Tom a warning of what he can expect if he behaves in a similar fashion to these men. Yet, amazingly, Tom doesn't take the hint. Instead of resolving to change his ways, he actually goes in the opposite direction: he makes a diabolical pact with the devil, selling his soul in return for Captain Kidd's treasure and a chance to make a great deal of money as a usurer, or moneylender.

One presumes that the hapless Peabody and Crowninshield also made the same deal with the devil. They should stand as a warning as to what will happen to Tom if he doesn't mend his ways. But Tom is so blinded by greed that he doesn't care. He is prepared to take his chances and jeopardize his mortal soul by entering into a pact with the devil.