In order to genetically modify a potato (or any crop or food) scientists have to change its DNA.   DNA is deoxyribonucleic acid which is in all of the cells throughout the potato, contains genes that give the potato its characteristics.

To understand the properties of DNA, look at this picture from the National Human Genome Research Institute.

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As this picture shows, DNA is shaped like a ladder.  This shape is called a double helix. The rungs of the "ladder" are called base pairs.  Certain sequences of base pairs, called genes,  result in a certain characteristics.  There are thousands of these genes for any food.   When a scientist physically changes a gene, it is called genetic engineering.  There are a few different ways to engineer genes.  They are: