Short version: Charles Babbage, after years of struggling to build an analog computer, designed an Analytical Engine (never built) which would have been numerical. He was not a good explainer and was difficult to get along with. Lord Byron's daughter, in the process of writing up an explanation of the Analytical Engine, saw aspects to how it would work (programming loops, etc) that Babbage either didn't see or couldn't articulate.
They communicated largely by mail, but with 5 times daily delivery that wasn't nearly as slow as you might think.
There are no dark secrets or thrilling escapades, but it is interesting, and Wolfram tries to imagine what might have been if Babbage hadn't been so prickly and if Ada hadn't died so young.