A zygote is formed when a male sperm cell and a female egg cell combine. This occurs during the end of the cell division process called meiosis.
There are two types of nuclear cell division: mitosis and meiosis. During the process of mitosis, DNA molecules condense and form long strands of chromosomes. The molecules replicate themselves and organize into identical pairs, on a double helix. The double strands then split in half, and two new separate cells are formed. Ultimately, the goal of mitosis is simply to replicate DNA molecules and create new cells.
Meiosis on the other hand, goes through the same replication process but adds an extra step. During meiosis, the double helix strands do not immediately separate, but wrap themselves around each other in a process called 'crossing over'. After crossing over, the chromosome pairs split into four separate cells, instead of two, as in mitosis. One of the cells become a female egg and the other cells eventually become male sperm cells: One sperm cell joins with the female egg to form a zygote. When chromosome strands cross over, they create a variety of DNA mixtures, which eventually translate into the resulting offspring's particular physical or behavioral traits.