A cell spends most of its life in the interphase stage of the cell cycle. This can be broken down into G1, (gap 1) S (synthesis) and G2 (gap 2) phases. Eventually,  after the cell passes through various checkpoints, it proceeds to the M phase (mitosis) when it divides and forms two genetically identical daughter cells.

In order for a cell to have enough DNA to be dispersed into two cells, the important step known as replication occurs. Since DNA is a double helix, either side of the molecule can serve as a template to be copied or duplicated to form its complementary strand, resulting in two identical DNA double helixes. 

This step occurs during the S phase of interphase. S refers to synthesis and it is the crucial time when the cell replicates its DNA so that a complete set can be placed into two daughter cells.

Please note: I have attached an excellent link to a diagram as one of my references below.