In Physics, escape velocity is the amount of speed needed to leave the gravitational influence of a celestial body.

But I saw a really nice adaptation of the concept to personal economy from the Humans of New York photographer:

His new objective is to bestow upon his subjects sufficient funds to obtain what he calls “escape velocity,” an astronomy term that he has adapted to mean “liberation from the gravity of their own circumstances.” In other words, Stanton has transformed his storytelling project into something that is part grant-giving operation, part one-man venture-capital firm, and part lottery.

So he wants to give the people he photographs an opportunity to leave their current circumstances by donating some money. Enough money to propel you into a better life = escape velocity.