The first open world Sonic game was Sonic Adventure 2, which was released for the Dreamcast in 2001.
These games typically give the player a large, explorable environment to explore, and allow them to travel freely between different areas. In the Sonic the Hedgehog video game franchise, an open world Sonic game refers to any game in which the player is free to roam the game world at will, without being constrained by linear level design.