Tarry (intransitive verb): 1 a: to delay or be tardy in acting or doing b: to linger in expectation : wait
2: to abide or stay in or at a place (Merriam-Webster)
Found on Page 1, paragraph 2 of “Young Goodman Brown”–>“Dearest heart,” whispered she, softly and rather sadly, when her lips were close to his ear, “pr’ythee, put off your journey until sunrise, and sleep in your own bed to-night. A lone woman is troubled with such dreams and such thoughts, that she’s afeard of herself, sometimes. Pray, tarry with me this night, dear husband, of all nights in the year!”
I believe this word in the quote means that Mr. Brown’s wife, Faith, did not want her husband to go out on his journey but to stay with her and spend time with her. Mr. Brown’s journey was going to be far, so Faith was wooing her husband to stay since she did not want to be left all alone.