The basic unit of heredity is a gene. A gene is a segment of DNA that codes for a specific protein or set of proteins. The DNA is configured into chromosomes, and each parent gives one of each chromosome to offspring.
The specific DNA sequence of the gene can vary between each chromosome, so offspring inherit different copies of the same gene from the mother and the father. Some genes are not very diverse, so offspring might get the same copy from both parents. The specific copies of each gene inherited determines which proteins are produced in the offspring. The proteins work in conjunction with one another to determine the phenotype of the offspring.