"50% of the variance in antisocial phenotypes is the result of genetic factors" means what?
In a population the phenotypic variance can be caused by several underlying variance including the variance in the environment and the genetic variance (among others). The fraction of the phenotypic variance that is caused by the genetic variance is what we called the heritability in the broad sense. The fraction of the phenotypic variance that is caused by the additive genetic variance is what we called the heritability in the narrow sense. 

So the sentence


  50% of the variance in antisocial phenotypes is the result of genetic factors.


can be rephrased as


  Antisocial phenotypes have a heritability of 0.5.


The concept of heritability is useful as it gives us an idea of how well selection can act on the changing the frequency of phenotypic traits in the population (see How to interpret the breeders equation?). Please have a look at Why is a heritability coefficient not an index of how “genetic” something is? for more information.