What's the difference between mitosis and meiosis?

Mitosis is the process somatic (normal body cells) use to divide. Two diploid (full set of chromosomes) daughter cells are produced from one diploid cell. In order for this to occur, the cell must replicate its entire genome before mitosis (this happens in S phase of the cell cycle). Mitosis is one stage of the cell cycle (the steps are G1, S, G2 then M). Mitosis is split into four stages: prophase, metaphase, anaphase then telophase. 

Meiosis is the process to produce gametes (sex cells). Gametes are haploid (contain half a set of chromosomes) so meiosis starts with a diploid cell and produces 4 haploid daughter cells. Because 4 daughter cells are produced, meiosis involves 2 rounds of cell division (so prophase, metaphase, anaphase and telophase all occur twice).