The protein part makes up the center of the nucleosome and consists of two H2A, H2B, H3 and H4 histone proteins. The DNA is wrapped around that protein complex in two turns, with each turn consisting of about 80 base pairs. Together with the DNA linking two nucleosomes, there are about 200 bp of DNA per nucleosome.
The main purpose of nucleosomes seems to be organization and packing of DNA. Stacked nucleosomes are called 10-nm-fiber and have a packing rate of ~6, compared to "free" DNA (per nm length). A chain of nucleosomes can be arranged in a 30-nm-fiber, a helical structure with a packing rate of ~40. This structure needs the H1 histone.