A racist term that is often applied to people of Pakistani or South Asian descent. Its origins are commonly traced back to about 30 years ago, when British hooligans used the term Paki-bashing to refer to the gang beating of ethnic minorities.
Today, it is commonly used by ethnocentric and insensitive white people who either:
a) cannot tolerate 3rd world immigration even though their forefathers colonized the shit out of Asia, Africa and the Americas;
b) want to make fun of immigrants who have left their homelands to seek a better living in the country that prospered from fucking up and stealing resources from said homelands;
c) are too stupid to realize that many immigrants do the menial jobs they themselves would hate to do;
Paki is also sometimes used by mistake as a short form of Pakistani. Even this is frowned upon though, as it is an indicator of a person's ignorance towards people of different cultures and nations. The most famous example of this "accidental" usage may be in a remark George W. Bush made in 2002 when asked about the nuclear rivalry between Pakistan and India.
Don't be fooled by the narrow-minded xenophobes who have attempted to explain this term - calling a brown person a Paki is just as derogatory as calling a black person a nigger.
"Go back to your country, Paki."
"Sorry pal, I don't think I'll be able to board a plane again thanks to your country's anti-terror laws. Looks like I'm here to stay. Shall we discuss William Shakespeare and Charles Dickens over tea and biscuits instead? That's what people do around here don't they?"