To deport is to kick someone out of a country. Deporting is also to deliver a person to the authorities of another country. Although you might like to deport your little brother from your room, it’s something governments do.
Governments have the power to deport. When you're deported, you get thrown out of a country, often because you were there illegally. This type of deporting is similar to exiling. Another form of deporting is even harsher: sometimes a person is not only tossed out of one country, but handed over to the government of another country. This is also called being extradited, and it usually happens to people wanted for a crime in the second country.