During mitosis a cell becomes two. Genetically, the two daughter-cells are identical to each other and to the original cell.
In single-celled organisms the daughter-cells separate. But in multicellular species the cells remain together. Mitosis therefore increases the number of cells in a multicellular organism.
This makes differentiation possible. In humans, for example, some cells become blood cells, some muscle tissue, some light receptors at the back of the eye, and so on.
Meiosis halves the chromosome number. In the course of meiosis a cell divides once, half its chromosomes going into each daughter-cell, and then each of these daughter-cells divides again in a manner rather like mitosis, so that there is no further change in chromosome number.
Meiosis is essential in any species that reproduces sexually. Sexual reproduction involves a combining of two gametes in the process of fertilization. Fertilization doubles the chromosome number. So there has to be one point in the life-cycle at which the number is halved again.
All sexually reproducing organisms must have one meiosis and one fertilization in each life-cycle.
The relative timing of meiosis and fertilization differs in different species. Humans, like many but not all animals, leave meiosis until gamete formation. This means that every cell in the life-cycle is diploid except the gametes.
In plants meiosis always forms spores. These divide by mitosis to form a number of haploid cells (very few in flowering plants, but more in simpler plants).
In some algae and fungi the zygote divides by meiosis, so that the zygote is the only diploid cell in the life-cycle.