Death is only the beginning in Bleach, and there are a lot of different spirit realms that one's soul can end up in the series. These alternate planes of existence operate on their own rules, and yet they also interact with each other in some very interesting ways. Where one's soul is ultimately found will have a major impact on the quality of a person's afterlife, and that's why it's important for Soul Reapers to do the job that they do: guiding spirits to the Soul Society.
Ichigo and friends discover these spirit realms as the story needs them, so it's possible there are even more out there than have been shown in the series. Still, there are only four major planes which play a role in Bleach, each with its own denizens, rules, and atmosphere. Here's what they are, why they're important, and how to get to them.
1 The Soul Society
The Soul Society is the spirit realm most frequently seen in the series. It's the place where Pluses (the souls of good humans) go when they die, and it's also the home of the Soul Reapers and other spiritual beings. The Soul Society is a massive place, with most of the action in Bleach focusing on the Seireitei and the city surrounding it. Life in the Soul Society is much like life on Earth, except that one can no longer die of things like starvation. The Soul Society has wealthy families of honored lineage and slums occupied by the poorest, as is shown in Rukia's backstory. Everything in the Soul Society is made up of Reishi, or spirit particles, as opposed to ordinary matter.
Given it is home to the Soul Reapers, the importance of the Soul Society is fairly obvious. One can reach the Soul Society in a variety of ways. For a Plus, a Soul Reaper can perform the Konso ritual, sending them there directly. Even Hollows can have their misdeeds forgiven through this ritual, but only those performed after becoming a Hollow. Soul Reapers have a special means of traversing between realms, making use of Hell Butterflies to open a portal referred to as the Senkaimon. Those without permission can also potentially enter the Soul Society through a dangerous border region known as the Dangai Precipice World, but more on that later.
2 Hueco Mundo
Hueco Mundo is the next most commonly seen realm and the setting of the eponymous Hueco Mundo arc. Hueco Mundo is the realm of Hollows, a land of eternal night and featureless deserts that lies somewhere between the World of the Living and the Soul Society. The most noteworthy location is Las Noches, effectively the "capital" of Hueco Mundo and the only place with any kind of structure. Life in Hueco Mundo is terrifying, as Hollows prey on each other almost as much as they do humans. Those Hollows who gain the most power in this way can become Arrancar, human-looking spirits with the abilities of a Hollow and a Soul Reaper.
Most spirits who end up in Hueco Mundo had major regrets in life that kept them from moving on to the Soul Society, slowly transforming them from Pluses into Hollows, as seen with Orihime's brother. Hollows can traverse between worlds by opening portals known as Garganta, traversing the void between realms with relative ease. These portals can even lead to the Soul Society, although most Hollows capable of that are smart enough not to. Hueco Mundo is a realm rich in spiritual energy, which allows even the weakest Hollows to survive without access to humans.
3 Hell
Hell is a special realm reserved specifically for the most depraved of souls. These individuals were evil while they were humans, and are sent to Hell as punishment. Arrancar and Soul Reapers can end up in Hell, too, if their power was too great, or their sins were too numerous. Little is known about Hell; it was focused upon in the fourth Bleach movie, Hellverse, but that movie is of dubious canonicity. Within canon, Hell is home to rare Hollows known as "the Beasts of Hell," which don't emit spiritual pressure and as such are highly dangerous.
When a being is sent to Hell, two massive doors appear, each with a skeleton on them, which open and drag the offending spirit inside. Unlike the other realms, it's not possible for anyone, even Soul Reapers, to travel to Hell and back freely. Once a spirit enters Hell, it's nearly impossible for them to leave it, at least for any significant period of time. The environment of Hell can cause radical changes to spirits who enter it, altering their appearance and abilities permanently. While souls in the Soul Society are eventually reincarnated on Earth, souls in Hell receive no such second chance, locking them out of the reincarnation cycle forever.
4 Dangai Precipice World
The last commonly relevant realm is the Dangai. It's a border region which exists between the Soul Society and the World of the Living. It resembles an endless pathway of some sort, and exists beyond the reach of time and space, such that hours inside in mere minutes outside. While it may look like a simple corridor, there's actually an intense flow of spiritual pressure and energy which can overwhelm any soul trying to through it. One of its most notable features is the Kototsu, an object which patrols the area and destroys anything it comes into with.
As the border region, it can be accessed from either the World of the Living or the Soul Society, although it too requires a Senkaimon portal to reach it. Because there's very little present, and it's a dangerous place, there's really not much reason for anyone–Soul Reaper, Human, or Hollow–to spend much time here. It did prove to be a good place for laying a trap, as Aizen kidnapped Orihime while she was traversing the Dangai.
That covers all four of the major spirit realms in Bleach. There are some smaller pocket dimensions which occasionally show up, such as the Valley of Screams, which branches off of the Dangai, or the Soul King's realm, which is connected to the Soul Society, but these are rare. The spirit realms are each fascinating places, well-developed and interesting for fans to discuss. Understanding these realms and how they connect and operate can make it a lot easier to keep up with the action in Bleach.