Having read first generation geek and knowing that my mom took Fortran as her foreign language in college, I would guess this is my generation (unless computer generations are supposed to be shorter than human generations.)
There are probably two ways to think about 2nd generation geeks. One follows the convention of Generation X, and labels peer groups by time period, dating from either the invention of the computer or the coining of the word geek. The second is a usage similar to "second generation immigrant" and indicates the number of generations that your family has contained geeks. I happen to fit both definitions (Hurray for Apple IIe and Basic!), but I will write about the second because I think it has had more effect on my life. After all, there are probably lots of people who can compile a list of 2nd generation geek traits (You might be a geek....), but how many of them have taken their parents to a science museum in Barcelona on a high school language trip? (True story. We had some free time and my parents didn't speak Spanish or Catalan, but they knew the science. The museum had a great Newtonian mechanics section with lots of hands on games. They puzzled out the signs from their knowlege of the physics.)
Being the second generation of geeks in a family is fun, because if the kids at school get too boring, (who wants to watch sports when you can talk about science or computer stuff?) parents are often willing to do fun things, such as help their child to take something apart, reinstall an OS, teach Morse code, or discuss the "Three Laws" (of motion, thermodynamics, or robotics.) While this can lead to a wonderful relationship with geek parents, it tends to make other kids look at you strangly ("You like hanging out with your parents? You're weird!") On the other hand, it works well for school trips, as they can serve as a chaperone without embarrassing their child.
I would imagine that both geekdom and childhood are more difficult when there is a mismatch, Thank God I was born to geek parents!