A U.S. visa allows the bearer to apply for entry to the U.S. in a certain classification (e.g. student (F), visitor (B), temporary worker (H)). A visa does not grant the bearer the right to enter the United States. The Department of State (DOS) is responsible for visa adjudication at U.S. Embassies and Consulates outside of the U.S. The Department of Homeland Security (DHS), Bureau of Customs and Border Protection (BCBP) immigration inspectors determine admission into, length of stay and conditions of stay in, the U.S. at a port of entry. The information on a nonimmigrant visa only relates to when an individual may apply for entry into the U.S. DHS immigration inspectors will record the terms of your admission on your Arrival/Departure Record (I-94 white or I-94W green) and in your passport.
Source: U.S. Citizenship and Immigration Services
An official endorsement on a document or passport denoting that the bearer may proceed.
Source: U.S. Courts
A citizen of a foreign country, wishing to enter the U.S., generally must first obtain a visa, either a nonimmigrant visa for temporary stay, or an immigrant visa for permanent residence. Visa applicants will need to apply overseas, at the U.S. Embassy or Consulate, generally in their country of permanent residence. The type of visa you must have is defined by immigration law, and relates to the purpose of your travel. A visa allows a foreign citizen to travel to the United States port-of entry, and request permission of the U.S. immigration inspector to enter the U.S. Issuance of a visa does not guarantee entry to the United States. The CBP Officer at the port-of-entry determines whether you can be admitted and decides how long you can stay for any particular visit.
Source: U.S. Department of State.