The Federation designation for the region of space containing the Sol system, best known as the site of the battle against the Borg in Star Trek: First Contact.
Sector 001 is the area of space that includes Earth and the rest of the Sol system. The term is first heard in the Next Generation story The Best of Both Worlds, in which the assimilated Picard, speaking as Locutus, states that the Borg cube will continue to Sector 001 after wiping out the fleet at Wolf 359.
It is most closely tied to Star Trek: First Contact. In 2373 a second cube fights its way to Earth, and the fleet that meets it there, including the Defiant under Worf, takes heavy losses. Picard brings the Enterprise-E against orders and directs fire onto a weak point that destroys the cube.
A sphere escapes from the wreck and travels back to 2063 to stop Zefram Cochrane's warp flight, and the Enterprise follows it.