Well, it is pretty straightforward - there is a bigger impact on the odds of the outcome for the continuous variable given which category you are in for the categorical variable. So if you have a gene and an environmental exposure, people with the gene have a greater odds of the outcome when also exposed to the same continuous variable as individuals without the gene. So the gene has an impact and the exposure has an impact, but when you have both there is a multiplicative impact (given you are using a product term to examine for interaction).