Apprehension: The arrest of a removable alien by U.S. Immigration and Customs Enforcement (ICE). Each apprehension of the same alien in a fiscal year is counted separately.
Cancellation of Removal: A discretionary benefit adjusting an alien’s status from that of deportable alien to one lawfully admitted for permanent residence. Application for cancellation of removal is made during the course of a hearing before an immigration judge.
Deportable Alien (INA §237(a)): An alien in and admitted to the United States subject to any grounds of removal specified in the Immigration and Nationality Act. This includes any alien illegally in the United States, regardless of whether the alien entered the country by fraud or misrepresentation or entered legally but subsequently violated the terms of his or her nonimmigrant classification or status.
Immigration and Naturalization Act: The Act (INA), which, along with other immigration laws, treaties, and conventions of the United States, relates to the immigration, temporary admission, naturalization, and removal of aliens.
Immigration Judge: An attorney appointed by the Attorney General to act as an administrative judge within the Executive Office for Immigration Review. They are qualified to conduct specified classes of proceedings, including removal proceedings.
Inadmissible Alien(INA §212(a)): An alien seeking admission at a port of entry who does not meet the criteria in the INA for admission. The alien may be placed in removal proceedings or, under certain circumstances, allowed to withdraw his or her application for admission.
Priority Date: In the USCIS Immigrant visa petition application process, the priority date is the date the petition was filed. If the alien relative has a priority date on or before the date listed in the visa bulletin, then he or she is currently eligible for a visa.
Removal: The expulsion of an alien from the United States. This expulsion may be based on grounds of inadmissibility or deportability.
Removal Proceeding:  An immigration court hearing to determine whether a noncitizen will be removed from the U.S.  Refers to all cases commenced on or after April 1, 1997.  Before that date, these hearings were called deportation hearings or exclusion hearings.
Voluntary Departure: The departure of an alien from the United States without an order of removal. The departure may or may not have been preceded by a hearing before an immigration judge. An alien allowed to voluntarily depart concedes removability but does not have a bar to seeking admission at a port-of-entry at any time. Failure to depart within the time granted results in a fine and a ten-year bar to several forms of relief from deportation.
Withdrawal: An arriving alien’s voluntary retraction of an application for admission to the United States in lieu of a removal hearing before an immigration judge or an expedited removal.

Note: Some information courtesy of the United States Citizenship and Immigration website.