Q:

Strong accents and rural areas correlation

(I'm not a linguist, just a Stack Exchange user who thought this site is the one for this question)
It is often the case that people living in rural areas (in any country) have a "stronger", less intelligble way of speaking. Why is this so? Perhaps because in smaller population it's easier for new words, new pronunciations to evolve?
It occured to me that it might not be the case at all, but that it appears to be so because we take the "urban way" as standard, and in reality, all are equally strong/intelligble. But I think that there really is an objective difference. Is there and why?

A:

This pattern does show up a lot, and there seem to be multiple factors driving it. Rural areas (though not only such areas) tend contain small, immobile, tight-knit populations, in which local identity is socially important and outside communication is (historically) limited. 
On one level, simple isolation means there's less exposure to the mainstream forms, and to the 'leveling' effect of contact between speech communities. Such conditions instead seem to favor the maintenance of non-standard language features, and resistance to incoming changes from the mainstream; in the face of incoming changes, such conditions may even promote a reaction of 'exaggeration' of non-standard, local-identity features. Socioeconomic class may often play a role, and rural areas tend to be poorer.
Note, though, that the conditions described have often applied equally well to dense, urban enclaves. In addition, as a general rule, isolation of regions has trended down over time (due to growth of transportation and communications technology). This breakdown of isolation seems to be the major factor in the loss of the distinctive local variety of e.g. Martha's Vineyard, or North Carolina's Outer Banks communities.

A:

Less intelligible to whom? I think what you are trying to mean with "accent" here is the form of "accent" that can mean either of three things: 1) a form of speech that differs from some standard, prescriptively more correct form of speech of the same language 2) a form of speech that differs from your own, but is still the same language 3) a foreign accent, where the speaker has learned the language as an adult and cannot pass for a native. Let's ignore 3). The first generally only holds for modern countries with a strong capital city, a high degree of centralization and/or mass media. Preferably all three. The second definition first occurred the moment the very first group of speech-using humans became two groups of speech-using humans, + about a generation of passed time.
Accent sorts under sociolinguistics for a reason. The intelligibility is, among other things, dependent on the status difference between speaker and listener - if, say, the listener considers him/herself to be of higher status, there is less of a penalty if the listener cannot understand the speaker. A low status person on the other hand might depend on being able to understand a high status speaker. Rural people are often considered lower status by people living in cities, ergo, rural people are unintelligible. Power games.
Moving away from the sociolinguistic side, read up on dialects as to why area-dependent accents differ. (There are also solely status-based accents, aka. sociolects, for instance those acquired through being stuck in a boarding school.) Dialects are accents turned up to 11, and is why one language can split into two or more languages given enough time.

