The original cell that divides is called the parent (mother) cell, while the two, new identical cells are called daughter cells. A cell normally divides into two new cells (once it has copied all its DNA). This process is called mitosis. Each new cell gets a complete copy of all the DNA, bundled up as 46 chromosomes.
The cell cycle (stages in a cell's life) is made up of stages in which the cell grows and rests, copies its DNA, and divides into two new cells.