Answer:
There are two main events during the cell cycle. Interphase and mitosis/meiosis (this will depend on the type of cell)
Interphase is the part of the cell cycle where the cell is pretty much "living its life" (growing, feeding, doing metabolism).
Interphase is divided in 3 main phases. G1-S-G2. (see attached picture)
During mitosis the cell will produce 2 new identical cells. Citocinesis is the part where the cytoplasm finally divides.