Other World is where souls go after they die in the Dragon Ball universe. Exceptional people, like Goku, get to keep their bodies.
Other World is also called the Other side or Cosmos or Next dimension of the living world. When any character dies, their spirit goes to the other world where King Yema decides the future of the souls - Hell or Heaven. If the spirit is good and did good things while alive, he will pass to heaven, on the other hand if the spirit is evil, he will go to hell.
The other world is known to be bigger than the living Universe. In the below is living world, above it is Hell, above it is Snake way, above it is Kai's realm. The world is governed by Kais and each of the Kais have their own separate planet who looks after the living Universe. The Kais also have levels, there are 4 lower level kais who looks after the Universe, the kai above them is called Grand Kai who looks after the lower level kais and observes Hell and Heaven, the kais above them is called supreme kais who looks after all of the kais below. In the latest Dragon Ball Z movie - Battle Of Gods, it was shown that not even the Supreme kais are the true rulers of the Universe, there are Gods who lives above them who creates and destroys creation. The environment of the other world is always daytime. Spirits have to take air plane to visit heaven.
After a person's death he/she are not allowed to keep their body. After death the spirits arranges in a line and meets King Yemma one by one to proceed further. Dead person's spirit can travel freely in some area. In some case, some people are allowed to keep their respective body if they die heroically to save their peoples in battle. In this case Goku is also allowed to keep his body and also allowed to go anywhere in the other world. He can travel to hell, Kai's planets and every possible area. Same things go for fortune teller Baba. She is also allowed to travel to the other world from living world. She is also allowed to hire dead heroic people for a day. Goku's adoptive grandpa Gohan and other fighters were hired by Baba from the other world. Dead people receives Halo at the top of their head.
As the other world is completely different than the living world, the nature system is also different. The fundamental physics such as Gravity, Force and a few materials properties are works as the living world. The people from Hell cannot escape from hell even if the sky is open. The clouds of Snake way which separates the hell from Kai's realm, is seems to change its properties like if a person tries to escape through the cloud it will react as solid object though it will act like normal clouds to other peoples who lives above hell. Time does not exist in the other world which was mentioned by Goku, for this advantage he could transform to Super Saiyan 3 easily while he was in the other world. In the living world Super Saiyan 3 transformation maintenance was difficult for massive Ki drains through time.
The heroic warriors who died to protect their peoples can train there under Kais. Each Kai has their own warriors from their own watch-over quadrants of the Universe. Some warriors train there for thousands of years. Most of the them stays on Grand kai's planet which is bigger than the lower level Kai's planets.
A martial-arts tournament is arranged by Grand Kai. Usually the tournament held in every 10 thousands years. But when North kai was died and all the 4 Kais gathered in Grand Kai's planet with their warriors, a special tournament was arranged and whoever wins the final match will receive training from Grand Kai himself.