Undocumented immigrants or illegal aliens, however you want to call them are immigrants who can not enter the U.S. legally, without proper documents. Such as, guest workers, students, and tourists. The rest of these people just slip across the border without showing a passport or visa to the border guard.
Undocumented Immigrants may be a threat to the nations' cultural and political integrity because they are multiplying and are comfortable with their culture and language and have no interest in changing them. So if they keep growing faster in population they will over run the country sooner or later, thus putting culture and language at stake. 8-13 million of these people are taking jobs from citizens, thus increasing unemployment rates in the U.S. Also if they keep up their growth, Native Americans will eventually disappear.
On the other hand, illegal aliens are also useful. They are useful to agricultural sectors, companies and other factories since they are cheap labor, thus making them wealthier.