The DNA is a two strand molecule. It is designed in a manner such that one part comes from the mother and the other from the father. Each piece is corresponding to the other, so, basically, each gene has two modifications. One is from the father and one from the mother. Now, if one of these genes is positive for a specific trait it is called heterozygous.
While, if both the genes are positive for a trait it is called homozygous. This helps to decipher the pattern of inheritance and also allows us to predict the likelihood of a certain disease occurring.