Migration has affected countries historically and contemporarily:
Effects on Country People are Emigrating From
People may leave their country because of a weak economy, overpopulation, or a bad job market. Sometimes there are few opportunities for more educated people which can lead to a brain drain, which is the emigration of well trained/intelligent people from their country of origin.
However, it can be good for the country's economy because it can open up more jobs for people. Also, the people who have emigrated can send remittances, which is money earned in their new country mailed back home.
Effects on Country People Are Immigrating To
Migration also affects the economy of the country that migrants are moving to. It is more people that need housing, education, employment, health care, etc.
But, it can be good for that country in that it diffuses culture and creates new jobs. Sometimes people are brought into a country because there are job openings that need to be filled.