While Tribeca sounds like a foreign word, it is not. Triangle Below Canal Street is its origin (no connection to the oh so gay Canal Street in Manchester, England). It isn't actually a triangle as it has four sides, but it is triangularly shaped with Canal Street being its northern border and the World Trade Centre area on its southern border. Isn't that interesting. Well, I think so and it turned out to be so easy to find out.
But the most common version traces it to the story of "Dutch Fred the Cop," a veteran policeman, who with his rookie partner, was watching a small riot on West 39th Street near Tenth Avenue. The rookie is supposed to have said, "This place is hell itself," to which Fred replied, "Hell's a mild climate. This is Hell's Kitchen.
In never understood New York geography until I went there.