Mitosis is the duplication and division of the nucleus, and produces two identical daughter cells during prophase, metaphase, anaphase, and telophase. Interphase is often included in discussions of mitosis, but interphase is technically not part of mitosis.
There are two reasons for mitosis: growth of an organism from zygote to adult, and repair of damaged or lost cells.
Here are the basics of each phase:
The cell spends most of its life in this phase because it's the only phase when the DNA is able to be read (it is called chromatin at this point). At the end of interphase, each chromosome is copied exactly and the two copies remain connected to each other.
The chromatin begins to coil up into more compact structures called chromatids. This prevents the chromosomes from getting caught and tangled with each other as they begin to move around the cell. Also, spindle fibers begin to form which will help move the chromosomes around.
The chromatids move to the middle of the cell, aka the equator. They will remain here until each pair of copied chromatids have reached the equator.
With the help of the spindle fibers, the chromatids separate from their copy that they had been attached to. Each chromatid of the copied pair will move to opposite ends of the cell.
A new nucleus forms around each set of chromosomes at the "poles" of the cell and the cell undergoes cytokinesis--the actual division of one original cell into two 'daughter' cells.
The cell cycle is normally halted after mitosis occurs and the new cells spend the rest of their lives in interphase. In this phase, the cell's DNA is in the form of chromatin (uncoiled and able to be read) and the cell performs it's function within the tissues of the organism.
If the cell cycle is out of control and a cell continuously undergoes mitosis, the cell no longer functions as part of its tissue, and to make matters worse it keeps dividing and producing more cells that are not functional to the organism. These abnormal cells are cancerous, and the mass of these rapidly dividing cells is a tumor.
When an individual "has cancer", that usually means that a tumor has grown to a certain size and some of the abnormal cells have left the tumor and have moved to another area of the body. A tumor that has not spread is called benign. A tumor that has spread to other areas (either through the blood stream or the lymph nodes) is called malignant.