Immigration

Immigration is the act of foreign people arriving into a country with the purpose of permanent residence.

Emigration, on the other hand, is the act of people leaving their homeland.

Both of these actions comprise migration.

Reasons
There is a lot of reasons for people migrating (usually into the more developed or more liberal nations), but the most common include:
 * Looking for a decent-paying job in a nearby country
 * Dislike of the home nation's government or the latest policies introduced
 * Fear of persecution in the home country (such migrants are called "refugees" or "asylum seekers")

Illegal immigration
In many countries, the immigration laws put limits and restrictions on who can migrate. These limits get easily broken by illegal immigrants -- those living and working in the country unofficially. Those employing illegals make use of this by giving them lower wages, worse conditions and threats of deportation.

Liberals usually stand for making immigration easier and letting more to work legally and pay taxes, thus helping create true competition on the job market. Conservatives, on the other hand, usually stand for tightening the immigration limits (not surprising, since employers profit from that greatly).