In order for something to be considered living it must have all eight life traits. One of those traits is the ability to reproduce. Mitosis is cellular reproduction- that is, mitosis accounts for the making of new cells.
In multicellular animals this cellular reproduction is used for growth and repair of the larger tissues and body. For example, without mitosis, you'd be "Johnny the One Celled Boy" since after your mother's egg cell was fertilized by your father's sperm cell, that resulting fertilized, single cell needs to reproduce over and over again to make you- a multicellular organism. This is the same with all living organisms. Also, if it were not for mitosis, cuts and breaks would never heal!
In single celled organisms, like bacteria and protists, mitosis is used for reproduction (which is still cellular reproduction) call Fission BUT the resulting cells are autonomous (individual and on their own) as they are made. Mitosis goes from one cell to two to four to eight to 16 to 32 to 64 to 128 to 256 and onward. This is one of the reasons that bacterial infections happen so quickly- the cells are multiplying (undergoing mitosis) at an exponential rate.
In order to understand mitosis you need to remember that the nucleus contains DNA. This DNA is roughly 6 feet long and needs to fit into the microscopic nucleus you saw in your cheek cells. To do that the DNA is repeatedly coiled and broken into pieces called chromosomes. Every living things has a diffferent number of chromosomes. Humans have 46 or 23 pairs (one set from mom and one set from dad).
So mitosis is part of the cell cycle. A cycle which includes the following; interphase, prophase, metaphase, anaphase, telophase, and cytokinesis.
Interphase: This is a state in which a cell normally exists. Its a state of a normal cell doing normal cell things like growing. When the cell reaches a certain size or is chemically triggered, at the end of interphase the DNA in the nucleus will copy itself- doubling. So a human would now have 92 chromosomes- this can't stay like this!
_____________________________________ Mitosis Starts Here ______________________________________
Prophase: The cell enters prophase with 92 chromosomes (46 copied). In prophase the nucleus dissolves and the chromosomes uncoil.
Metaphase: During metaphase the 46 pairs of chromosomes line up, roughly in the middle of the cell, and another cell organelle (the centrioles) starts sending out spindle fibers.
Anaphase: The spindle fibers reach out and connect with the centromeres (the middle of the chromosome pairs) and start to pull the 46 pairs of chromsomes apart in anaphase. The, now two, sets of chromosomes make their way to the sides of the cell.
Telophase: Telophase finds the two sets of 46 chromsomes coiling back up and clumping together. A new nucleus starts to form around EACH of the groups of chromosomes so that the single cell now has, not only, 92 chromosomes but two nuclei!
_____________________________________ Mitosis Ends Here ______________________________________
Cytokinesis: Mitosis is now over. The animal cell splits in two. The plant cell forms a cell wall down the middle of the cell. During this splitting or dividing of the cell, the other organelles get "trapped" in one cell or another. At the end of this process there will now be two cells; each with an identical copy of the set of chromosomes.
NOTE: I have used human numbers of chromosomes here for this example. In reality, the number of chromosomes is dependent on the living organism.