People are unique because one person's DNA differs from every other person's DNA. Even identical twins have very slight variations, according to About.com, although it's perhaps due to chemical changes that occur within their DNA as they age.
Humans have about 99.9 percent of their DNA in common, according to the Smithsonian National Museum of Natural History. The remaining 0.1 percent is unique among individuals, and it's that unique DNA that differentiates one person from the next.
DNA stands for dioxyribonuclean acid, which is a molecule found in the nuclei of all cells contained in living things. When cells divide, the new cells contain the exact same DNA material as the cells from which they came. This material consists of genes, which the National Institutes of Health's Genetics Home Reference describes as units of heredity. Genes, in turn, are made up of DNA chemical bases. The four bases are adenine, guanine, cytosine and thymine. They're referred to by their first letters: A, G, C and T. The bases serve as a genetic code.
Sugar and phosphate molecules attach to bases to form nucleotides. Strings of nucleotides make up DNA's double helix shape. The order of bases along the nucleotides establish all the information about a person. Unique base ordering among individuals accounts for the individuals' uniqueness.