Mitosis and meiosis are both forms of cell division in organisms. Although there are differences in the two processes, they are both very simple to understand and absolutely essential to life. Both take place only is Eukaryote cells (that is, cells with membrane-bound organelle. Non-bacterial cells).
Let's start with mitosis.
The process of mitosis is a five step process of nuclear division (the division of a cell's nucleus). The five stages, in order of sequence, are:
1) Prophase: in this stage, the cromatin (genetic material inside the cell's nucleus) condenses and forms rod shaped structures called chromosomes.
2) Prometaphase: Microtubules which have extended from the two centrosomes located at the opposite poles of the cells begin to cross the nuclear space within it while the nuclear membrane dissolves.
3) Metaphase: The condensed chromosomes line up along the center of the cell.
4) Anaphase: The chromosomes begin to move to opposite ends of the cell, stretching it out until the cell pinches off into two new cells, call daughter cells. Each daughter cell is genetically identical to the parent cell.
5) Telophase: The "clean up" phase. The chromosomes go back to being chromatin in the newly formed nucleus. The cell is now back to a normal state and the division is complete.
Now, let's tackle Meiosis.
This only occurs in haploid cells, which are sex cells (ex: sperm).
Meiosis is a two part cell division that results in the production of cells with only half the number of chromosomes as the original parent cell. This is done in two stages called "Meiosis I" and "Meiosis II". Very original names, I know.
Before you get too overwhelmed, I have some good news. 'Meiosis I' is absolutely the same as mitosis. Those five steps that I mentioned above all happen again here. Nothing changes. The only difference is at the end where an additional step, called interphase takes place. This step bridges Meiosis I and Meiosis II.
In Meiosis II, the cell divides in a similar way, except that there is no replication of chromosomes. Instead, the chromosomes are shared between the two daughter cells so that each cell has half the number of chromosomes as the original.
For example, in humans, every cell has 46 chromosomes. However, sperm cells in males and egg cells in females, only have 23 chromosomes (half of 46) because they are the result of meiosis. When the sperm and egg fuse together, they come a single cell with a complete set of 46 chromosomes.