The word "nigger" is a derogatory term for a person with dark skin, especially someone of African origin. It is a variation of the old racial classification "Negro," which comes from niger, the Latin word for the color black. Some historians think the word "nigger" started as the phonetic spelling of the Southern pronunciation of "Negro."
Most people consider the word "nigger" to be a racial slur, but it has recently been reclaimed within some parts of the African-American community as a term of endearment. In hip-hop and rap culture, for instance, "nigger" is almost always shortened to "nigga" or the plural, "niggaz" or "niggas." It's most often used by one black person to claim another black person as their friend or family (e.g., "my niggas"). Songs like Biggie Small's "Niggas" begins with a callout "To all my Brooklyn Niggas."
But the term is still very controversial. Whether it's considered offensive or not seems to depend very much on context. When white rappers--like Eminem--or film directors--like Quentin Tarantino--try to use the term nigger and its variations in a non-perjorative way, there tends to be more of a public outcry than when an African-American like Puffy does so. Ironically, they are accused of being "wiggers," which is short for white niggers.