The short version is that it means you could use another supply of the same type to hit 240V.
Imagine two 9V batteries (floating voltage sources) connected in series. You could get 18V from the outside terminals, or +9V/-9V with the shared terminal acting as ground. Now if the same two batteries had their negative terminals referenced to earth ground (think connected to a chassis, for example) then you're stuck with a 9V supply, albeit at twice the current.
Floating in this sense means that these supplies act like batteries. If you took two of these supplies (or two sections of a dual supply) and wired them in series you could get double the voltage safely. The protection circuitry within is likely not designed for more than 240VDC, so if you wire a higher voltage supply than that you must ensure that it's not ground referenced, i.e. that the whole circuit is never referenced to ground. I'd avoid mucking with voltages that high if you can help it.
In the end, ground is where you say it is. Earth ground is, for the most part (wiring losses, lightning strikes, and dry soil aside) an absolute reference on the scale of a building, so it's handy to reference to.
As a side note, most nixie tubes won't require more than about 80V to trigger. See
here or
here for details. Be gentle with nixie tubes, they have a finite lifetime and are no longer being manufactured!
Hope that helps.