Howdy, where Turbs got the information in post #2 comes from this site, which really explains further what a 120/240 volt SPLIT phase 50 amp service is and how it operates. The keyword here is Split, as in two 120 volt legs)
If you will click on the 50 amp tab, on the page linked above, the author explains how a 120/240 split phase service works, and how it all stays 120 volts.
I also advise clicking on the outlet testing tabs too, to familiarize yourself how/why you should be testing any outlet before plugging in (your house or campground).
This is another site that explains the 50 amp split phase service too.
Electrical Tutorial - Chapter 3 - 30 Amp versus 50 Amp