Alternative hip hop is a form of hip hop music that is very different from gangsta rap, crunk, and snap. A way to explain it would be that if "regular hip hop" was on the middle of a number line, gangsta rap, crunk, and snap would be on one side, and alternative hip hop would be on the other. Even though it is a form of hip hop, fans of alternative hip hop tend to also be fans of horrorcore more than "regular hip hop" or especially R&B.
Alternative hip hop originally came from the United States, and some artists like Gorillaz sprang up from the United Kingdom. Examples of American alternative hip hop artists are Talib Kweli, Mos Def, (and the band they started together, Black Star), Common, Nas, Kanye West, A Tribe Called Quest, Jurassic 5, and Styles of Beyond. It started as a movement-of-sorts from hip hop artists against the "tasteless" hip hop that was popular in the 1990s.