what is the contribution of charles babbage in the modern day computer?

Answer 1

He came up with the idea of creating a machine to perform mathematical calculations, in the same way that modern machines perform millions and millions of mathematical calculations a second today.

Answer 2

dead_elves (answerer 2) is not quite right. Babbage's Difference Engine would have performed a particular automatic sequence of mathematical operations, but no other sequence.

In his Analytical Engine, different sequences of operations could have been prepared on perforated cards, and the machine would have stepped its way through whichever sequence was loaded into it from time to time. One possible sequence would, of course, have been that of the Difference Engine! The Analytical Engine was never built, but it contained the first idea of programmability.

Answer 3

He basically designed the first computer, the Babbage Difference Engine, which was the very first programmable device. He never built it, but if I remember correctly , a bunch of scientists actually built a working prototype from his plans a while ago, proving that it would have worked.