>>971
I always see people asking about this but I'm always terrible at explaining it myself. All it is is a shortened/informal form of の+です following a verb (in your examples, though it can be used after nouns, etc.)
http://www.guidetojapanese.org/particles3.html#part5
Has a really good explanation on the whole thing, it's the whole section on the bottom of that page (The 「の」 particle as explanation).
It's not a request or a demand, more of an added point of explanation, and usually it doesn't really have its own translation. And yes, it's used quite often in real Japanese, I see/hear it daily spoken and written. Hope that helps.