The process described is cell division, which involves the replication and separation of chromosomes. Before cell division can occur, the DNA must be replicated. This happens in the S phase of the cell cycle. The cell also goes through the G1 and G2 phases, which together with the S phase are collectively referred to as interphase.
The first stage of mitosis is called prophase, where the chromosomes condense and the nuclear envelope disappears. Following prophase is metaphase, where the sister chromatids align on the equatorial plate. Anaphase is the next stage, during which the sister chromatids separate and move to opposite poles of the cell. Telophase follows, during which the chromatin expands, the nuclear envelope reappears, and two nuclei form.
After mitosis, cytokinesis occurs, during which the cytoplasm divides and the cell splits into two daughter cells. It is important to note that mitosis occurs in eukaryotic cells, while prokaryotic cells undergo a similar process called binary fission.