I also had this same problem some time back and was trying to figure out what all of this (nibbana) meant. This may sound cliche, but the only way to understand what it, is to really see it. Or at least glimpse it. And the only way to do that is to understand anichcha, dukka, anaththa and keep looking at the world with that understanding.
I was trying to explain the cooling down feeling to a friend and realised that it is very hard to explain it, as the words I was using had very different meanings in a worldly sense.
As Lal has explained in his post, the best way to explain it is through the extinguishing of a fire. When a candle is extinguished, the wax, the wick, the oxygen is still there but the light / fire is no more. So the fact that the fire is no more is something that we can see in this world but, then again the “lack of the fire” is not really in this world too. Again it is very hard to explain as we are using worldly concepts.
Hope this helps.