Step 1: Understand the cell cycle. The cell cycle is the set of steps a cell goes through to grow and then divide. It has a long interphase followed by the M phase (division).
Step 2: Name the parts of interphase. Interphase is split into three parts in this order: $G_1$ phase, then S phase, then $G_2$ phase.
Step 3: Look at the $G_1$ phase. In $G_1$ the cell grows bigger and makes proteins and organelles. No DNA copying happens here.
Step 4: Look at the S phase. The letter S stands for Synthesis. In this phase the DNA copies itself, so the genetic material doubles and each chromosome forms two sister chromatids.
Step 5: Look at $G_2$ and M phases. In $G_2$ the cell gets ready to divide, and in the M phase the actual division (mitosis) takes place. No DNA copying happens in these.
Step 6: Conclude. So DNA replication takes place only during the S phase. \[ \boxed{\text{S phase}} \]