When you are looking at how genetics and environment influence intelligence you are looking at the topic of nature versus nurture. The nature side of this debate is the biological make up of a person, this would be their genetic predisposition to the ability to process their environment and to develop intelligence. There are several biological diseases that can affect intelligence such as Downs syndrome which affects genetic make up and can affect a child's cognitive development.
When you are looking at the nurture side of intelligence you are looking at how the child's environment can have an effect on a child's ability to process information in their environment and develop intelligence. An example of this would be a looking at a calm nurturing environment in which a child can develop secure attachment as opposed to a high stress environment in which a child does not observe appropriate behavior to model and is not able to develop secure attachment. These two environments will cause a child to develop very different neural pathways as well as how they interact with their enviroment.