English, mainly in US, from Hebrew "gift"; OT Ruth 4:22, 1 Samuel 16. Chambers suggests the meaning: "God is".
This ancient name, in recent years most famously borne by Jesse James, a Missouri outlaw, is now occasionally rendered as Jessie in the US. This is probably a reflection of the female name spelt thus, although there is no clear connection between the male and female names. It is interesting to note that, of the two main organisations celebrating the life of the outlaw, one spells his forename "Jesse" and the other uses "Jessie".