Anyone who is not a citizen of the United States requires legal permission, granted by the U.S. Department of Homeland Security or the U.S. Department of State, to enter, remain, and travel in the United States. The permission that a foreigner receives to come to the United States is normally granted through the issuance of a visa. A visa is normally provided to the applicant in the form of a card or a document, but sometimes is merely an endorsement in the foreigner's passport.
Visas are typically distinguished between two main categories: immigrant visas and non-immigrant visas. Immigrant visas are for people who intend to remain in the United States on a permanent basis as residents. Only certain categories of people are eligible for immigrant visas, or green cards. For that reason, most foreigners interested in coming to the United States must explore the option of applying for a non-immigrant visa. There are currently over 20 types of non-immigrant visas, but the most common kind of non-immigrant visa is a tourist, or visitor's, visa--the B1/B2 visa.
Some people who wish to enter the United States are considered to be "inadmissible" because they have certain immigration or criminal violations on their records. The majority of people who have been deported, or who have received a voluntary departure, will be inadmissible to the United States for one reason or another. When people are inadmissible to the United States, they nevertheless may be able to apply for and obtain visas, but they will also need to apply for the correct waiver (or waivers) of inadmissibility before they will be allowed to re-enter the U.S.