The Eclector was the main ship used by Yondu's clan of the Ravagers serving as a port to the M-ships. The ship was destroyed during the Escape from the Eclector, but the third quadrant become the new headquarters of the Guardians of the Galaxy.
Deal with the Guardians
Star-Lord and Gamora were taken to the Eclector after being abducted by the Ravagers. Once on board, they were interrogated by Yondu Udonta, whom they convinced to help them defend Xandar from Ronan the Accuser's upcoming attack on the condition that Yondu would get the Orb once they had won. Rocket Raccoon, Drax the Destroyer and Groot then arrived in the Milano and threatened to blow up the Eclector with the Hadron Enforcer before Quill alerted them that they had reached a deal.
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The three then boarded the vessel and the Guardians and Ravagers began planning for the upcoming battle. The Eclector fired a large ball of energy at the Dark Aster, distracting the Sakaarans for the attacking M-ships to get by undetected.
A couple months after the Battle of Xandar, the Yondu Ravager Clan was hired by Ayesha, the leader of the Sovereign Race. She ordered the Clan to recapture the Guardians, of which they managed to get Rocket and Groot after losing some of their men. However, when Taserface, one of the Ravagers, wants Peter Quill, Yondu didn't want to turn him in. This causes Taserface to take the three hostage and stage a mutiny, becoming the new leader of the Ravagers and ejecting Yondu's loyalists to die in outer space while Nebula cuts off Yondu's fin.
But on the Eclector, Groot had managed to find a new fin for Yondu, taking advantage of the fact that he wasn't trapped in a cell with them. Yondu and Rocket then break out of their cell, with Yondu later using his fin to kill Taserface's loyalists with an arrow. After a lot of the loyal Taserface supporters were dead, Yondu sets the Eclector to blow up and escapes with Rocket and Groot using the Third Quadrant, but not before Taserface was able to send Yondu's coordinates to Ayesha at the moment he blew up with his ship.