Unlawful presence in the United States can affect an applicant in many different ways. 

 The Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (IIRAIRA) created the "3- and 10- year inadmissibility" bars for individuals who are unlawfully present in the United States.  The overall consequence of being "unlawfully present" are:

1.  If in the U.S., and applying for a nonimmigrant visa, prohibit an applicant from changing and/or extending status in the United States.
2.  If outside the U.S., prohibit an applicant from obtaining a visa (nonimmigrant OR immigrant) at the U.S. Consulate/Embassy.
3.  If in the U.S., and applying for an immigrant visa "green card," prohibit an applicant from adjusting status in the United States ("bar to adjustment").

Basically, overstaying a period of authorized stay, normally noted on the I-94 form stapled into your passport, can have serious immigration consequences.

If you are in this situation you will be required to request a waiver, if available.