Jefferson had some bad vibes about Burr and so had him replaced by George Clinton as his VP.
The legend of the Burr Conspiracy states that he wanted to take a chunk of Texas, Mexico, and Louisiana Territories, then referred to as "the West," and build his own Empire using an army of farmers and recruits with ideas of secession.
He had some powerful and rich friends to lend him support.
Burr-stick'em's homies included, but were not limited to, dudes with names like Blennerhassett and Marquis de Casa Yrujo. Blennerhasset, from what I know, is not a Main Dude of History, but has an island in the Ohio river named for him. He had a zany secret laboratory cum mansion on said island, and according to wikipedia that is where he met Burr. Marquis of Casa Yrujo was a fiery little ambassador who was well connected. They were the financial backbone of the Burr Conspiracy.
Burr went to his old army pal, General Jimmy Wilkinson for muscle. JayWilks had a serious booze problem, but he was commander in chief of the US forces, and could mobilize heat at a moment's notice, free to move about the largely unsettled Louisiana territory as he pleased. Burr had convinced Jefferson to name Wilkey as Governor of The Louisiana Territory. When it came time for the United States to strike out against Spain, who also laid claim to the lands to the west, Burr would take control of the disputed lands of Mexico under the guise of US actions. He attempted to recruit men and ships from the British, in exchange for some of the lands he was planning on taking from the US. He even tried making a few deals with the Spanish.
But eventually his cover was blown. Wilkinson turned in a coded message known as the Cipher Letter to the courts, and laid out Burr's plans without directly naming him. But rumors of Burr's deviousness had already begun to spread throughout the country, mainly because of his own recruitment campaign. There was a price on his head, and eventually he was arrested under charges of treason. His effigy was burned in the streets, his face was on all the papers, and he was basically labeled as a wicked crazy dude.
He was acquitted, mainly because what his plans were didn't fall under the Constitutional definition of "treason."
He fled the country, traveling around Europe trying to hatch all kinds of kooky schemes, and eventually wound up in New York practicing law in obscurity.