Babbage never finished the Difference Engine. Before it was completed he started work on the Analytical Engine, which could be programmed using punched cards. In 1843 Babbage asked Lovelace to translate a French article about the Analytical Engine by an Italian engineer named Luigi Manabrea. While translating the article, Lovelace added copious notes of her own -- including the first step-by-step sequences of operations for solving certain mathematical problems. It was these sets of instructions that have led to her be called the first computer programmer.
Lovelace also saw potential in Babbage's machines that he may not have seen himself. As Smith and Webb write on Google's official blog, "While Babbage saw [the analytical engine] as a mathematical calculator, Ada understood it had much more potential. She realized it was, in essence, a machine that could manipulate symbols in accordance with defined rules, and -- crucially -- that there was no reason the symbols had to represent only numbers and equations. ... This was an astounding conceptual leap from calculation to computing."