A dark-skinned person from Pakistan, India, or other parts of Southeast Asia. It is really odd that this word is considered derogatory, since "paki" means "pure" in the local language (Urdu).
There's even more to the story of the name of the country. It was invented by a political writer in 1934, using letters from five districts of what was then all part of British India. The "P" came from Punjab, the "A" from Afghania, the "K" from Kashmir, the "S" from Sindh, and the "tan" from Baluchistan. So a "paki" is not what most people think.