There are two questions here. 1) What is genetic variance? It is actually clearly defined. 2) How does sexual reproduction generate more genetic variation?
What is genetic variance?
Assuming bi-allelic loci, just assign a value of 0 to one allele and 1 to the other allele. Then compute the variance! Average this value over all loci. Done! Have a look at any intro book in quantitative genetic for more info (see here)
How does sexual reproduction generate more genetic variation?
You are right "sexual reproduction only "reshuffles" alleles, and doesn't generate new ones". It is a common misconception that sexual reproduction generate genetic variation. The details of whether it does or it does not depends upon the detailed distribution of dominance coefficient and distribution of epistatic effects.
There has been a lot of work on the subject and it is not an easy work to summarize it. Sally Otto does a great job to summarize this misconception in her speech On the Evolution of Sex and the Advantages of Recombination. You should definitely have a look at it.
Note however, in some species that preforms both asexual and sexual selection, it happens that sexual selection is coupled with higher mutation rate than asexual selection. In such cases, sexual selection does indeed increase genetic variance but only so because of tis correlated effect on mutation rate.