Mitosis is a type of cell division which occurs in somatic or vegetative cells.
In mitosis parent cell divides and forms two progeny cells.
Both the progeny cells contain equal number of chromosome as parental cell, hence called equational division.
Meiosis is a type of cell division which occurs in germ cells.
In meiosis parent cell divides and forms four progeny cells.
In all the progeny cells, chromosome number gets reduced to half, hence called reductional division.
Yes, plants go through mitosis and meiosis both. During their vegetative growth they undergo mitosis and during sexual reproduction (for the production of spores) they undergo meiosis.