As a reference, the eNotes site is not an essay writing site. The purpose of the site is to provide answers and help to questions posed by students, teachers, or others needing help on subject specific topics.
That being said, what I can offer is an explanation of what a Narrative essay is and how to go about writing one from the perspective of a sailor aboard the Mayflower.
First, a narrative essay is an essay in which the writer tells a story. For a great link, try out the Purdue OWL site linked below.
As for the essay itself, what you are going to need to do is create a character, or a persona, who would have lived in 1621 and was a sailor aboard the Mayflower. (The site below offers a wonderful list of people actually on the Mayflower.)
In the essay you should tell the story of your character's life in chronological order as they prepared to board the ship, what life was like on the ship, and how it felt to land in America. One of the key characteristics of the narrative is to provide many details that include imagery which appeals to the senses. What you want is for your reader to be able to see, feel, hear, taste, and smell the different things a sailor on the Mayflower would have sensed.