A congregationalist minister and prominent Christian lecturer, Appleton was notably determined to make Bowdoin students more pious.

He worked at the school, right before it reached its full prominence in the 1820s, when Nathaniel Hawthorne, Henry Wadsworth Longfellow, and Franklin Pierce attended.

Elizabeth was the daughter of Stewartstown, County Tyrone, Ireland born Robert Means (1742–1823) and Mary McGregor (1752–1838).

Together, Jesse and Elizabeth were the parents of five children who survived through infancy, including: Appleton died on November 12, 1819, in Brunswick, Maine.

[6] Through his daughter Mary, he was the grandfather of William Appleton Aiken (1833–1929), who in 1861 married Eliza Coit Buckingham (1838–1924), and Mary Appleton Aiken, who in 1868 married Francis H. Snow (1840–1908), a professor and chancellor of the University of Kansas who became prominent through the discovery of a fungus fatal to chinch bugs and its propagation and distribution.