Obama World is a nickname adopted by 065 TYMB, a Young Money, Black Disciples set located in Chicago, Illinois. The name Obama World was adopted after one of TYMB's member nicknamed Obama was murdered. Obama was a drill rapper, and has some songs on youtube.
It's very common for Chicago gangs to adopt name for fallen members, for instance the name TYMB, was adopted by this particular Young Money, BD set after one of their member named TY was murdered.