The USA as a country mainly started in the East, when all the people came across from Europe and landed on the Eastern shore. The areas where these people landed became colonies, populated by different nationalities like English, Dutch, German etc.
As you can imagine these colonies were pretty lawless and there was much in fighting, as well as fighting with local indian tribles.
Gradually these colonies turned one by one into states, but they only existed on the eastern side of the USA.
In fact if you look at where the American Civil War was fought it was all down the East side of the USA. Almost no fighting took place in the centre or on the West.
The Spanish travelled up the Western shore from South America (which is why all the Western cities have Spanish names like Los Angeles and San Francisco).
But the huge middle of the USA was owned by the French and had no states. These had huge areas called "territories" ("indian territories") which were pretty wild and had no law or government so it was "every man for himself".
Eventually the French decided to sell this land to pay for a war, and the land sale was called the Louisiana Purchase where over 800,000 square miles were sold.
http://en.wikipedia.o...ki/Louisiana_Purchase
This huge mass of land then became part of the USA and this led to a massive migration West by people wanting a better life, particularly after the gold rush in California.
The huge move west by people into "wild" areas with no law or government I think gave rise to the name "wild west". Many indian tribles lived on this land and they did not take too kindly to seeing all these new people arrive taking their land and killing their buffalo, and this led to many many wars between the people migrating and the local indians.
There was also much fighting in the South West (New Mexico, Texas etc) as the USA grew (the Alamo etc) and this also probably helped give rise to the term "Wild West".
Ever since the USA was "discovered" by the Europeans it has been mostly a gradual move West across the huge land mass, so I suppose the "wild" bit was always 50 miles West of where civilization had reached at that point.