Set in a dystopian future, the PSP game depicts the struggle between the aragami, divine creatures that have suddenly decided to attack the planet, and the God Eaters charged with taking them down. Your characters (who work in teams of up to four people, online or off) use a set of divine weaponry, called "deus ex machina," to suck the life essences out of these aragami and make it their own -- letting them power up their offense, converting their weapon between blade, gun, or powerful "predator form."
Judging by the initial media, God Eater is...well, basically Monster Hunter. No better way to describe it. In the Japanese announcement Namco Bandai suggests obliquely that the game is much faster-paced than MH, but we'll have to see about that. It's due out this fall in Japan; a US release has yet to be announced.