According to Wikipedia, "She knew and was taught by Mary Somerville, noted researcher and scientific author of the 19th century, who introduced her in turn to Charles Babbage on June 5, 1833. Other acquaintances were Sir David Brewster, Charles Wheatstone, Charles Dickens and Michael Faraday.
During a nine-month period in 1842-1843, Ada translated Italian mathematician Luigi Menabrea's memoir on Babbage's newest proposed machine, the Analytical Engine. With the article, she appended a set of notes which specified in complete detail a method for calculating Bernoulli numbers with the Engine, recognized by historians as the world's first computer program. Biographers debate the extent of her original contributions, with some holding that the programs were written by Babbage himself. Babbage wrote the following on the subject, in his Passages from the Life of a Philosopher (1846).
'I then suggested that she add some notes to Menabrea's memoir, an idea which was immediately adopted. We discussed together the various illustrations that might be introduced: I suggested several but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.'
Lovelace's prose also acknowledged some possibilities of the machine which Babbage never published, such as speculating that 'the Engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.'
Ada met and corresponded with Charles Babbage on many occasions, including socially and in relation to Babbage's Difference Engine and Analytical Engine. Their relationship was not of a romantic nature.
Ada was one of the few people who fully understood Babbage's ideas and created a program for the Analytical Engine. Had the Analytical Engine ever actually been built, her program would have been able to calculate a sequence of Bernoulli numbers. Based on this work, Lovelace is now widely credited with being the first computer programmer...
The computer language Ada, created by the U.S. Defense Department, was named after her. The reference manual for the language was approved on December 10, 1980, Ada's birthday, and the Department of Defense Military Standard for the language, 'MIL-STD-1815' was given the number of the year of her birth.
Her image can be seen on the Microsoft product authenticity hologram stickers.
The British Computer Society annually awards a medal in her name."