What is a series of events that cells go through as they grow and divide?

The series of events that all cells go through is called the Cell Cycle. In this cycle, there are 3 phases, Quiescent or the resting stage, Interphase when the cell is gathering nutrients and preparing for the final stage, Mitosis. Mitosis consists of 5 phases
Prophase, metaphase, anaphase, telophase, and cytokinesis. This is when the cell replicates its dna, organs, and other necessities and at the end splits.

Meiosis and mitosis 
Meiosis is the process by which one diploid eukaryotic cell divides to generate four haploid cells often called gametes
Mitosis is the process by which a cell duplicates its genetic information (DNA) , in order to generate two identical daughter cells .