DNA is organized into chromosomes, which are millions of bases pairs long.  Each chromosome is divided into kilobase-pair-long genes which contain instructions for making proteins that carry out important functions in the body.  Proteins play a key role in executing almost every conceivable function in humans, including oxygen transport, food digestion, cell signaling, and even wiggling your toes!
So why are genes so important for learning about our ancestry?  Well, they are responsible for our physical traits, such as eye color, freckles, and hair type, to name a few.  As a result of sexual reproduction, humans inherit 23 chromosomes from each parent.  Depending on which genes are inherited, offspring receive some traits from the father and some from the mother.  Thus, our genes are passed on from generation to generation, which is why family members often resemble each other.