Final answer:
The organized pieces of DNA within cells are called chromosomes, which are vital for efficiently carrying genetic information and are typically packed into 46 structures in humans.
Step-by-step explanation:
The organized pieces of DNA are called chromosomes. Within the cell nucleus, DNA is wrapped around proteins known as histones to form nucleosome complexes, resembling beads on a string. These nucleosomes help in the packing and organization of DNA. When cells prepare to divide, this material condenses even further into chromosomes, ensuring genetic information is efficiently divided and transferred to daughter cells. It's critical for DNA to be organized into chromosomes to allow cellular processes to access and utilize the genetic material properly, and humans typically have 46 chromosomes with about 22,000 genes distributed among them.