In eukaryotic organisms (organisms that have internal membranes for separation of organelles) DNA replication occurs in the cell nucleus during the "S phase" of the cell cycle.
In animals, After the DNA replication the nucleus membrane in collapses and a chromosomes are separated (in bacterium this chromosomes separation occurs without nucleus membrane collapsing). Also in this stage ("M phase") all the double organelles of the cell and the cytoplasm are being divided and two daughter cell (identical cells) are created.
# The DNA replication, (and also the replication of all the other organelles) is necessary in order to create a duplicate cell, with all the necessary information and processes of a normal cell.
From each cell you replicate, you get two identical cells - and so on.