A variation on death metal, also known as "Melodeath." Bands in this genre seem to have borrowed many of the traits of thrash, and combined them with classical death metal. For instance, these bands tend to have longer songs, more guitar melody/solos, and much more diverse lyrics. Blast beats are used, but not quite as often as they are in the more classical style of death metal. Vocals tend to be a mixture of the higher black-metal-style growls and the lower death-metal-style ones. Some of the newer bands have even been making limited use use of clean vocals (i.e., Profane Omen, Absence, Chimaira). As far as the mood...this style tends to be a lot less doomy than black metal (i.e., more lively, and not so depressing).
It can be argued that this style began with the band Carcass and their release of the album called "Heartwork." Carcass was originally more of a Grindcore-type band, but slowly refined their style, and progressed into a more and more melodic form of metal, until "melodic death metal" or "melodeath" was born. Since then, hundreds of bands have come about exhibiting many of the same qualities, such as In Flames, Dark Tranquillity, Arch Enemy, Fear My Thoughts, Shadow, Light This City, The Autumn Offering, etc.
Melodic Death Metal rules!