Much like a community in real life -- a group of "people" (usually) with common beliefs, A BGP community "is a group of destinations which share some common attribute" - RFC 1997.
There are numerous BGP communities, but basically it is translated and interpreted as a 32bit value. BGP communities are optional transitive attributes meaning they are not required and they can be passed on to other AS only if the router(s) decides to do so.
These are the well-known communities. More being suggested and drafted in other RFCs.
INTERNET - By default all destinations are assigned this community.
NO_EXPORT - Do not send the route to any eBGP neighbors.
NO_EXPORT_SUBCONFED - Do not send the route to any sub-confederations.
NO_ADVERTISE - Do not send the route to any neighbors (iBGP or eBGP).
LOCAL-AS - Do not send to anyone other than your LOCAL-AS (So this will prevent the router from sending to sub-confederations).