It means that the power supply's output must not have a connection to the AC socket's ground pin (internally to the power supply). It has nothing to do with using different sockets.
In other words: Use a power supply that comes with with a two-prong power plug, not a three-prong one.
The third prong on a power plug is the ground connection.
If you're from Europe, you have to use a power supply that comes with an Euro plug (which has only two contacts), not a Schuko plug (which has three contacts).
Note that you should not just try to disconnect the ground connection from a power supply that's usually connected to a three-prong (or Schuko) plug. Doing that is dangerous; you may get a shock.
The reason why the power supply should not be grounded is fairly simple: The device itself is already grounded. If you ground it both at the device and at the power supply, you create a ground loop. (If any point of a connected circuit is grounded, the entire circuit is grounded, and you don't really want to ground it twice.)