I find this method very valuable. It kind of ties into the discussion about blockers also.

Let's say I have two pair and my opponent I put 100% on either a set or an overpair. I beat the overpairs and the sets beat me - should I continue? It's important to know whether the set or the overpair is more likely. Let's say the board is T-high so 4 overpairs are possible (6 combinations each - total of 24 combinations) and of the 3 cards on the board 2 of them are paired with a card in my hand. This leaves 3 + 1 + 1 hand combinations of sets - total of 5. In this example my two-pair hand acts as a blocker for some of the sets but none of the overpairs.

This method with practice allows you to do quick sanity checks on hand combinations for different parts of an opponent range and have them lend the correct weight to your decisions.

Visualising it is just one way - but it's important to know this information on one level or another:
Two unpaired cards have 16 combinations
Two paired cards have 6 combinations
Two unpaired offsuit cards have 12 combinations
Two unpaired suited cards have 4 combinations
Two unpaired cards with one blocker have 12 combinations
Two unpaired cards with one blocker on each card value has 9 combinations
Two suited cards with blockers for each card value of the same suit have 3 combinations

etc etc - much easier than memorizing this whole litany of possible configurations is using something like what Spoonitnow described. It doesn't have to be graphical - I'm sure Spoon isn't thinking in colours - the mind can understand structure quite well.

I'm not saying you have to do it the way Spoon suggests - but taking this kind of information is into account is something you HAVE to do - one way or another.