Standard deviations aren't that bad; summation notation just always looks messy.
I assume N is the number of elements in the set. Basically, it's just telling you to take each x, subtract the mean value, square it, and multiply by the corresponding probability of that x. Add whatever you get for x(1) to what you get for x(2), x(3), x(4), ..., up to x(N). Then, multiply by whatever N' is.
In the denominator, you're just adding the probability of each x together, and multiplying that whole sum by (1 - N').
I'd need to see the fine print for the definition of the other variables, but summation notation is just an easy way of writing repetitive operations; in this case, you start by computing the value where i =1, add it to the value where i = 2, add that to the value where i = 3, and keep going up to the value i = N. It really only starts to get ugly when you get summations of summations >.<