The Bleachverse, or the world of Bleach, is not a universe, but a multi-verse rather, comprised of a number of vast dimensions, each with their own traits and populations.
Bleachverse Primary Dimensions:
Living World: also known as the World of the Living, or 'real world' to those without knowledge of the afterlife, this is the earthrealm, where mortals live, and spirits await their escort to Soul Society. To put it plainly, the living world is the core of the Bleachverse, where weak mortal souls tend to spend most of their time. Ever since the hellbreak in 1986, Japan has become the most spiritually active region, and host to the most spiritual conflict.
Soul Society: or heaven as you might call it, is the proper afterlife, where most souls are bound to go after their death, and await reincarnation in their new lives. Soul Society is the pivot dimension of the Bleachverse, which souls call home between lives, and where the Shinigami dwell.
Bleachverse Secondary Dimensions:
Hueco Mundo: in the vast boundary between the Living World and Soul Society lay the barren wastes of Heuco Mundo, a land rich in spirit-energy maintaining the barrier between life and death. It is in this dimension that Hollows make their home, which serves as the gateway dimension of the Bleachverse.
Hell: This dimension of torment serves as a 'prison' of sorts for evil souls, holding and punishing them for a time, before releasing them back into the living world in the hopes they will reform. Very few ever do.
King's Realm: The dimension into which the Spirit King has sealed himself and his palace. Serving as a counter-balance, this dimension is the glue that holds the hell dimension together, keeping the demons at bay.