A streaming world is one where there are no 'level' boundaries. Older games have forced you to enter an elevator or walk through a door, to mask the 'loading' phase where the current level was removed from memory and the whole of the new level was loaded. This gave a very disjointed feel to the game world. Modern open world games allow you to roam the entire world with no intermediate 'loading' stages by gradually loading new assets as they are approached. So even if the world is very huge, the memory usage can be managed by keeping a 'working set' of assets loaded at any time, in order to render only the objects most relevant to the player.
