An illegal immigrant is an immigrant who lives in a country without permission or in a way that is not allowed, or illegal. Millions of people around the world live in another country against the laws of that country.
Many of these people migrate to a country in secret. Many others come to the country legally as a visitor, then stay in the country when they should go home. Many of them work illegally and live in bad conditions. They move for pretty much the same reasons as other immigrants, but they don't legally have the right to be there.