Adding to the answer above, I would also point out the irony of Faith's questions and Goodman Brown's reply given the context of the entire story. Depending upon how literally or how allegorically one is reading the story, Faith's question can cause us to read multiple meanings. In some ways, her question seems to foreshadow the "evil" that Goodman Brown will witness this night and could even be read as a kind of "warning." Of course, Goodman Brown chooses to reject this warning and, over the course of the story, he turns away from both his wife and his faith.
The irony of Goodman Brown's reply is also important. His reply seems to suggest that this will be the last or only night he will venture away from his wife and/or his faith. However, we know that is not the case as the experiences of this night--whether or not they were real or imagined--will forever alter his relationship with his wife and his relationship with his faith.
Since Hawthorne's "Young Goodman Brown" is an allegorical story, the reader must find meaning within this context. For, it is Faith who asks Goodman (whose name suggests "everyman") to remain at home on "this night,...of all nights in the year," the night on which the Black Mass in the primeval forest is to take place. Faith does not wish for Goodman to place himself in the path of tempation by attending the Black Mass; she would rather that he just continue to believe in his Puritanism and remain with her rather than testing his faith.
As it is, of course, in his sanctimony, his "excellent resolve for the future," that Goodman feels "himself justified in making more haste on his present evil purpose"; he feels that his faith is strong enough to resist any temptations. So, he tells Faith to say her prayers, and no harm will come to him. Significantly, this statement of Goodman's wife foreshadows what will happen. By leaving his wife, Faith, Brown forsakes his belief in the godliness of humanity.
Are you just asking about the literal meaning of this sentence? If so, all that Young Goodman Brown is saying is that he cannot stay with his wife on this night. To "tarry" means to stay, to spend time. So if he must "tarry away" from her, that means that he has to stay or to spend time somewhere else.
Later on in the story, we see that Brown needs to go into the forest to meet with the devil. We do not know why he has arranged to meet the devil, but the devil is going to show him that various people that Brown has trusted or looked up to are (it appears) sinners. This is why Brown has to tarry away from his wife.