Both mitosis and meiosis are cell cycles. Mitosis gives a faithful reproduction of the genetic material where daughter cells are (barring mutation) clones of the original mother cell. A common misconception is that only diploid cells can undergo mitosis. Haploid cells are perfectly capable of dividing mitotically as well.
Meiosis differs from mitosis because the daughter cells have half the number of chromosomes. It's a critical step in sexual life cycles; without reducing the number of chromosomes either before or after gamete fusion, the number of chromosomes in the cell will become unmanageable. Typically we think of diploid cells as always being the mother cell. Agriculturally important crops like wheat, barley - and almost every major plant - have endoreduplicated chromosomes. Potatoes, for example, are tetraploid in the sporophyte generation (4n=48) and after meiosis the cells have two of each chromosome (2n=24) - thus sperm and egg are both diploid!