The proper definition of a rural area is, it is a   geographic area that is located outside towns and cities.
Who gave that definition?
That's just a general one but a more specific one by Health Resources and Services Administration of the U.S. Department of Health is  it is all population, housing, and territory not included within an urban area.
So what are we interested in by the definition you gave?
One thing i can tell you for sure is that  any place that is not urban is considered rural
Really, can you tell me more about rural area
Yes I can do that, a typical distinguishing factor is that they usually have  low population density and small settlements.
What is settlement?
A typical example is  Agricultural area