Heritability is an idea originated in breeding, and it is interesting mainly for breeders. It is defined as the part of the variation for a trait in a population that is due to genetic variation (in contrast to enviromental variation).
The heritability is useful for a breeder because if the variation observed in a population is mainly due to enviromental factors the trait won't be improved by selecting the best individuals in the population.
However, the concept is usually misunderstood. First, it always depends on the population studied. One trait could have high heritability in one population, and low in another because different populations can have different genetic variation. Moreover, for a particular population it also depends on the environment because is the fraction of variation not due to the enviroment, and that, of course, depends on how variable is the environment.
Moreover, calculating the heritability, in practice, is very difficult even in controlled environemnts and populations, and when it is calculated most of the time is restricted to heritability in the narrow sense, taking into account only aditive effects. (This basically means ignoring all medelian gene interactions).
What the heritability does not mean is how much a trait depends on the genes. That idea does not even makes sense because any trait will depend on many genes even when it has no heritability. For instance, the number of fingers in humans has a very low heritability, because most of the variation is due to the enviroment (e.g. accidents), but the number of fingers clearly depends of many genes.