What is behind "Would you like a cup of coffee?" in your country?
To clarify my question a bit,I'd like to present here a story out of my personal experience.
Once,I was working with my colleague for my client.He, the client, was German by nationality, and work took place at his home.There was nothing special- the quiet and usuall routine.We talked in German and were very delighted and pleased by ourselves.Just like good old friends.Then, after a while, the client asked us:"Would you like a cup of coffee?" Haven't been paying much attention or letting myself any solid deliberation,I just answered:"Sure.Why not?"..And we got our treats.The same procedure occured twice during our work...
How was my embarrassment when I unintentionally overheard complain to his suddenly coming back wife:"They drank the whole four cups of our coffee!!!And yet,by doing so, they said:'Schmeckt gut!!!'(Taste good!!!)";)
As enlightened me later, in such situations I must have politely refused his proposals,but who did know then? Is it conflicts of mentality? Funny enough,because in Russia it means a false hospitality. Either treat your guests(if you wish), or do not mention it at all. What does mean this question in your country? Is it a part of etiquette to ask or it is your real intention?

Question

What is behind "Would you like a cup of coffee?" in your country?
To clarify my question a bit,I'd like to present here a story out of my personal experience.
Once,I was working with my colleague for my client.He, the client, was German by nationality, and work took place at his home.There was nothing special- the quiet and usuall routine.We talked in German and were very delighted and pleased by ourselves.Just like good old friends.Then, after a while, the client asked us:"Would you like a cup of coffee?" Haven't been paying much attention or letting myself any solid deliberation,I just answered:"Sure.Why not?"..And we got our treats.The same procedure occured twice during our work...
How was my embarrassment when I unintentionally overheard  complain to his suddenly coming back wife:"They drank the whole four cups of our coffee!!!And yet,by doing so, they said:'Schmeckt gut!!!'(Taste good!!!)";)
 As enlightened me later, in such situations I must have politely refused his proposals,but who did know then? Is it conflicts of mentality? Funny enough,because in Russia it means a false hospitality. Either treat your guests(if you wish), or do not mention it at all. What does mean this question in your country? Is it a part of etiquette to ask or it is your real intention?

Answer

Yes, same here in Australia - if we offer a guest coffee we must be prepared to give it with pleasure.  Of course it's politeness to offer your guest a beverage, and I wonder if your friend was too intent on acting polite than actually giving coffee.

Reminds me of some advice a Slovak friend gave me (about Slovak culture): if I'm a guest and I politely decline coffee/drinks/food from my host, it's expected that I do not refuse the third time they're offered.  That would make me a rude guest.

Bit of a game, isn't it? :)

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In my country,coffee is expensive.So we use tea instead,if we use coffee,it probably means that you come at a wrong time that the hosts are enjoying the bribes they recieved from their subordinates.Only valid in places like a small city.

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I enjoyed reading your experience. ^^ 
In Argentina, coffee means a chance to share the whole week news with friends or meet new people. Cafés are popular here, in Buenos Aires specially. Though, it is not common to invite for a coffee at home. Instead we invite people to stay a little more and have a barbacue or finger food with us.

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haha... I don't know so much about German or Russia or about your mates. 
here in Japan we don't finish the dish or your tea/coffee when you're a gust for that reason you don't want make the host busy or don't act like you were there for coffee or foods but not for the meeting up. (nobody visits you just for the foods and coffee but it's the politeness of minds I think.) and the host always prepare for coffee before the cup becomes empty. so probably never be asked for another cup of coffee because the cup will fill with another before it's asked. You would probably ask the guest for another beverage when a cup of coffee is about to finish. There're always another a cup of coffee situations but that would be something very common for everybody for us I think. I would do the same for my close friends and family, too if they are the guests of mine.

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The Germans are a funny lot. 

If you come to my house and I offer you a cup of coffee, my question would mean "Do you want a cup of coffee?". 

Simple.

And as my guest you can have as much coffee (or tea, or beer, or whisky) as you want!