Although we would think that the idea of community is a really obvious one, it is very slippery. If you look at the scn.org link, you will see someone going through thousands of words trying to figure out what community is and is not. However, it's probably not enough to just say that it's hard to define community...
I would say that a community is a group of people (who can be living in proximity to each other or not) who share some sense of common identity. This is the basic idea of the definition given in the eNotes link.
What this means, though, is that community can be exceedingly hard to define and can mean many things, even if wouldn't really think those things have much in common. For example, my family could be a community because we share a common identity as a family. At the same time, all the people who support a given sports team could be a community. So could all people who identify as evangelical Christians. The list could be endless.
So this is a very hard thing to define. At its heart, though, a community must be defined by the sense that its members have -- a sense of having something in common with one another.