There are three airports in the Milan area, but if someone mentions Milan airport they are likely to mean Malpensa, which is the biggest. This airport is over 100 years old and is still named after the old farm on whose land the first small airport was built.
Malpensa is about 40 km from central Milan and is mainly used for long haul and budget international flights. It has the largest amount of international traffic in Italy apart from Rome. It also carries a large amount of cargo and is still expanding - in 2012 a third runway was built.
Linate airport, though much smaller is an important airport for domestic flights because it is much closer to the city than Malpensa - less than 8km. It also carries short haul international traffic.
Orio al Serio is nearer to Bergamo than Milan, and is often used by low cost airlines.