The name of the cell cycle phase where the cell grows and prepares for division is called the interphase. This phase consists of three sub-phases: G1 (gap 1), S (synthesis), and G2 (gap 2). During interphase, the cell undergoes significant growth, duplicates its DNA, and prepares essential proteins for mitosis. The interphase is crucial for ensuring that cells are properly equipped for successful division, promoting cellular reproduction, and facilitating tissue growth and repair. Any errors during interphase can lead to cell cycle disruptions and potential health issues like cancer.