As he drives around the city, we hear Travis' musing in his diary:
"Loneliness has followed me my whole life. Everywhere. In bars, in cars, sidewalks, stores, everywhere. There's no escape. I'm God's lonely man."
As screenwriter Paul Schrader was aware, Travis didn't actually come up with the term "God's Lonely Man…"
It actually comes from the title of an essay by the great American author Thomas Wolfe, and Schrader included a quote from that essay at the beginning of his screenplay:
"The whole conviction of my life now rests upon the belief that loneliness, far from being a rare and curious phenomenon, is the central and inevitable fact of human existence."
Travis, then, is a kind of archetype of the lonely person—he is "Man apart" as the poet James Wright phrased it. He's "God's lonely man" but his defining quality is the fact that he embodies separation from God and humanity and pretty much everything except for his own sense of anger. He completely embodies loneliness as "the central and inevitable fact of human existence" and shows its awful consequences—a descent into madness and violence.