Being "genetically predisposed to" a health problem means that you're more likely to have that problem than most people because the problem runs in your family:

Some people are genetically predisposed to certain kinds of cancer.

This phrase sounds academic or scientific.

The word "genetically" comes from "gene", which is a piece of information that is passed from parents to children. Some other ways that we use "genetically" are:

• A genetically modified organism is a plant or animal whose genes have been changed by scientists.
• Identical twins are genetically identical because they have the same genes.

Being "predisposed to" something just means that that thing often happens. You can use it like this:

That breed of dog is naturally predisposed to violence.

I'm predisposed to believe people when they tell me something.