As the land near the USA-Mexico border is mainly very hot desert, the people who try to illegal cross the border on foot often become very sweaty. As a result, their backs are wet with sweat and they are known by this feature.
In 1954, the U.S. Immigration and Naturalization Service made the word "wetback" official by naming the mission to remove illegal immigrants from the United States, Operation Wetback . In response to the increase of immigrants during the early 1950s, the agency developed the program to force immigrants (particularly Mexicans) back to their home countries. Aproximately one million Mexican Americans were deported in one year.
Today the term "wetback" is often used to express animosity towards Central American or Latin American immigrants--legal and illegal--who do not speak English. Meanwhile, in an attempt to reclaim the word, some Mexican-Americans call themselves Los Mojados, meaning "the wet ones."
~ This definition courtsey of www.gurl.com
Ed : Take it easy, man. He came over here as a baby on his mother's back. It's not his fault.
"Damn Robin's a filthy wet back!
....yeah so's Dolly man"
"That guy's a bit too wet back for my liking"