You are a courier, and you've been a courier for a long time. Being a courier is just a metaphor for being a RPG player. You go between places, and travel the world. You take jobs which you are usually not emotionally attached to. You deliver messages or physical packages between places. Because of your occupation, you are nomadic and don't really have a place to call home.
In the past, before the Divide is the way it is now, there used to be a supply route which directly linked the Mojave to the Western regions of the United States. The player is supposed to have come from there. There was a town along that route which was independent and born out of old world dreams. A place which believed in a more traditional America, than what the NCR offered. Avellone has commented that it was not an Enclave town, so it was likely non-military.
This town was a place that Ulysses believes was of a personal importance to the player. This might or might not be true, and it might or might not matter. Again, this is a metaphor for how in RPGs, when you wander the game world, you are drawn to certain central locations which are a) unique, b) developing communities. The player is not meant to have actually actively founded this community, instead it is suggested that through your actions (ie: a ton of random fetch quests) you helped the community survive and build up, even though you might not be fully aware of how important your actions are.
At some point, you deliver a package to the town and you leave. You don't know what was in the package, and you didn't care, because it was just another job. The origin of the package is unknown, but the contents were a sort of unlock key (either a robot, or some remote device) which activated the various facilities under and around the town. Various missile silos and military terminals. What happened after was a serious of underground nuclear explosions from the nukes, which tore the ground apart and filled the sky with radiation. Many more nukes remained intact, suggesting that the entire area was a huge nuclear weapon arsenal from before the war.
Ulysses is a Legion scout and assassin. He was from the East, and he was once part of a tribe called the Twisted Hair. They were absorbed by the Legion and destroyed, like all other tribes. He was the scout who first found Hoover Dam and reported it back to Caeser. He was also the one who commanded the White Legs to destroy New Canaan. At some point he was assigned to become a courier, to infiltrate the system and to keep tabs on the flow of items and information.
That's when he got interested in you, and the town you kept going back to. At first he saw it as a target for Caeser. But then later he found the idea of a new budding community so powerful that he wanted to leave the Legion and just stay there. He was the only survivor when the package your delivered was activated, because the Medical Eye-Bots saw the old world flag on his coat, and saved him.
After the destruction of what he saw as his last chance for a new life, he started wandering aimlessly, looking for answers. It was only after he saw your name again, that he decided to let you carry the chip instead, so he could watch and see what happens. He's been watching ever since, and then after you finally decide to pay $9.99 for Lonesome Road, he contacts you directly to lure you into the Divide since he's sick of waiting.