The differences between immigrate emigrate and migrate?

One immigrates into a country. One emigrates out of one's country. Migrate is usually used for animals and birds that move to other regions on an seasonal basis. Migrate can also be used when people move within a country, eg. from the country to urban areas.
Migration is movement from one area to another.

Immigration is entering one area from another.

Emmigration is leaving one area for another.