From the Super Mario Wiki
The Special World is a secret area in Super Mario World that can only be accessed by a secret Star Road in Star World. The levels are located in various environments and are designed to be much more difficult to clear than all the other levels in the game. The names of the levels are also peculiar for Super Mario World stage names; they are all based on surfing slang (including Tubular, Mondo, and Way Cool). If Mario and/or Luigi clear all the levels, a new Star Road will appear and transport the plumber back to Yoshi's Island, more specifically Yoshi's House. However, upon returning, the season will change from spring to fall (changing the color scheme of the environment), and several enemies will be completely transformed.
The symbol at the top of the Special World is the Super Famicom logo. It is also the logo used for the PAL version of the SNES, which retained the original Japanese console and controller pad design and colors. In the GBA version, the player can still see the SNES logo at the top left corner.
When playing the GBA version, completing the Special World will not transform the overworld, since that will only happen if the player finds the 96 exits. When the Special World is completed in Super Mario Advance 2: Super Mario World, the Special levels will have records of the player's highest score in that level. A message stating that the player will receive a special present upon completing the Special World appears in Super Mario Advance 2: Super Mario World; this is obstensibly referring to the overworld transformation.