I should've just googled the better definition for you:
http://tinyurl.com/tt4se
(from uscis.gov)
Included among the immigration benefits the USCIS oversees are: citizenship, lawful permanent residency, family- and employment-related immigration, employment authorization, inter-country adoptions, asylum and refugee status, replacement immigration documents, and foreign student authorization.
The reason people usually marry in US culture is called 'love', although that is not a requirement for a valid marital union in immigration-talk. The social or other benefits a US citizen gets from being married to another person are wide and varied.. and there is (or is not, depending) a tax consequence for being married, as well as legitimating children and all the other blah blah attached.
When a non-US citizen marries a US citizen, they do not become a US citizen automatically. In fact, immigration wise, nothing happens to them or for them until the US citizen initiates the petition I mentioned above.
To become a US citizen, an alien (simply a non-US citizen) must become a Legal Permanent Resident first. LPRs have a document called a Green Card to show their status.
Once a person has been an LPR for 5 years (and meet the other requirements), they can APPLY to become a US citizen, a process called Naturalization.
If the alien is the spouse of a US citizen, that 5 years is reduced to 3 years as an LPR (plus other requirements). This is what my husband did; he immigrated to the US based on our marriage, lived in the US for 3 years as an LPR and naturalized to US citizenship.
If an alien has entered the US illegally (not inspected), their path to even becoming an LPR is more difficult and time consuming.
If an alien entered the US legally but overstayed their period of legal admission, their overstay time is forgiven and they can legalize their status if they are married to a US citizen.
There are essentially 9 ways to become a Permanent Resident of the US, outlined in this article:
http://britishexpats.com/wiki/Pulaski's_Ways:_How_to_Live_and_Work_in_the_USA
An alien in the US legally or not must have a basis to start their immigration (outlined in the article). Someone who comes here as a visitor for example, can't simply apply to be a resident without a qualifying basis.