Basically what Gould meant by contingency was that the evolutionary paths of species were so dependent on conditions throughout its history that if you could rewind the "evolutionary tape" of any species and play it back, results would almost certainly never be the same. If you wound it back far enough, there's no certainty that intelligent life would evolve and if it did, there's no certainty it would turn out to be the same small branch of hominids we happen to occupy. Here's the man himself:
History includes too much chaos, or extremely sensitive dependence on minute and unmeasurable difference in initial conditions, leading to massively divergent outcomes based on tiny and unknowable disparities in starting points. And history includes too much contingency, or shaping of present results by long chains of unpredictable antecedent states, rather than immediate determination by timeless laws of nature. Homo sapiens did not appear on the earth, just a geologic second ago, because evolutionary theory predicts such an outcome based on themes of progress and increasing neural complexity. Humans arose, rather, as a fortuitous and contingent outcome of thousands of linked events, any one of which could have occurred differently and sent history on an alternative pathway that would not have led to consciousness.I've adopted the concept to how I think about lots of things in life. It certainly helps me to not regret the past. Like everyone, there are things I always thought I'd do differently if I could. But I also know that I'm very happy in my life now. Using contingency to frame my thoughts of the past, I know that if I changed one thing in my past, it's highly likely I would not wind up "here" again. I think that when you can accept the past, it makes it much easier to be happy in the present.