Common words:
* migrate: to move from one place to another, especially for a specific reason (like for food or breeding)
* migrant: a person who moves from one place to another, especially for work or to find a new home
* migration: the process of moving from one place to another, especially for a specific reason
Less common words:
* migratory: relating to migration
* emigrate: to leave one's country to live in another
* immigrate: to come to live permanently in a foreign country
* migraine: a severe headache, often with nausea and vomiting (the connection to "migrate" is a bit obscure, possibly relating to a sensation of movement)
Note: The spelling of the root word can vary slightly depending on the word.