From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Training Island (修行 の 島, Shugyō no Shima; FUNimation "Training Island"; Literally meaning "Island of Training") is an island located south of Turtle Island.
Turtle Hermit took his students here to train them because Turtle Island was not large enough to accommodate their needs. Turtle Hermit had the Kame House transported by Hoi Poi Capsule to this larger island.
Son Goku and Kuririn spent a lot of time on it before the 21st Tenkaichi Tournament "training" by delivering milk across the whole island, moving dirt, swimming, dodging Bees, and doing school work, which actually helped to fortify their muscles and minds at the same time. Training Island had a population of at least 300 people. A jungle on the island had many animals living in it. It was in this jungle that Roshi threw a rock for Goku and Kuririn to find. Goku and Kuririn were shown carrying milk in several different climates, such as desert, arctic, and others. It is unknown if the island really did have those different features or if it was just comic relief. The island was also the battle site of Yamucha and Tambourine in an anime filler during the King Piccolo Saga.
Dragon Ball Z
Training Island is the first level with enemies in Dragon Ball Z: Attack of the Saiyans, although you only travel through a cavern on the island. As a final test, Turtle Hermit tells Kuririn, Tenshinhan, and Yamucha to find a Crystal Ball that his sister, Uranai Baba, had given to him. The three students get to the Crystal Ball only to be confronted by Jackie Chun. After being defeated, Jackie Chun flees and the three take the Crystal Ball back to Turtle Hermit at the Kame House.