From the Super Mario Wiki
A World is a group of levels in Mario games. In Super Mario Bros. and Super Mario Bros.: The Lost Levels, each world always has exactly four levels, and in Super Mario Bros. 2 each world has three (except the final level, which only has two). However, starting in Super Mario Bros. 3, most games have a varying number of levels. In some three-dimensional Mario games, worlds are no longer used; now each level stands alone (but each level is sometimes referred to as a world), and the missions are either referred to as stars or episodes. In earlier games, worlds were simply numbered "World 1", "World 2", etc. In Super Mario Bros. 3, they have distinct names. Super Mario World has no clear separation of worlds on the world map.
In general terms, a "world" refers to any large area of land and space marked off from other regions. As such, "world" may refer to a politically or geographically distinct region of land (such as Desert Hill or Chocolate Island), a planet, or even an entire galaxy.
List of Worlds