Mitosis allows somatic [body] cells like skin cells to replicate their DNA; there are 46 chromosomes composed of 92 sister chromatids attached at the centromeres. During anaphase the 92 sister chromosomes are divided into half and dragged to opposite halves of the cell, creating 92 daughter chromosomes, 46 in one half and 46 in the other. During telophase the skin cell pinches off, leaving 46 chromosomes in each new cell.
One way to think about it is, if mitosis kept cutting the # of chromosomes in half, our skin cells would have 46, then 23, then 12, then 6, then 3, then 2, then 1, etc. chromosomes and eventually become devoid of genetic material. Since this doesn't happen we know that body cells must keep the number of chromosomes the same before and after mitosis.