Bruce Springsteen - Born To Run Lyrics Meaning

"In the day we sweat it out on the streets of a runaway American Dream":
The American Dream is to own a house; to have a place of your own, a place where you belong. But, the price of that dream is usually a 30-year mortgage, tying you to a place, and a job, and so this dream is somewhat compromised - trading in the freedom of youth for a lifetime of conformity and repetition for pursuit of that "dream".

"Sprung from cages on Highway 9":
This line must have taken him a while to think up. It changes the whole meaning of the first verse of the song. As opposed to something like "burning rubber down highway 9", it really underscores that cruising/street racing is the one last vestige of freedom, the one place they can break the rules and feel like individuals rather than part of the labor force. Out there, in their "chrome-wheeled, fuel-injected" machines, they are "sprung" from their working class prisons.
Later on in the song, he exposes this activity as an illusion of freedom with the line "hemi-powered drones". The cars are drones, just like the people are - cruising up and down the boulevard, weekend after weekend, it's the same routine and repetition of their daily lives.

"Everybody's out on the run tonight but there's no place left to hide."
A metaphor for being trapped. Everyone hops in their cars and goes cruising, but they aren't really going anywhere, just expressing subconsciously their urge to get out, and wherever they go, they see people just like themselves, trapped just like they are.