Most of it is smell
Why Does Coffee Smell Better Than It Tastes?
Coffee's aroma has about eight hundred separate compounds in it and its taste has only bitter and sour, so the nose does nearly all the work.
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Step 1 of 5
Roasting invents the smell.
A green coffee bean smells of almost nothing. Roasting drives a reaction between sugars and proteins that creates hundreds of aroma compounds that were not there before.
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Step 2 of 5
Aroma reaches you two ways.
Once through the nose from the cup, and again up the back of the throat while you drink. The second route is most of what people call taste and is easy to prove.
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Step 3 of 5
Bitterness is the tongue's whole contribution.
The tongue reports bitter, sour, sweet, salty and savoury. Coffee is essentially only the first two, which on their own would be nobody's favourite drink.
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Step 4 of 5
The aroma escapes fast.
Those compounds are light and volatile, which is why a fresh cup smells strong and a cold one smells of very little. Ground coffee loses most of its smell within days.
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Step 5 of 5
Block your nose and it is nearly gone.
Pinch your nose and drink, and coffee is bitter water. Let go and the whole thing arrives at once — which is exactly what a heavy cold does to it.
Caffeine is bitter on purpose. The plant makes it to put insects off eating the leaves, and it works on them far better than on us.
The short version
Coffee is mostly aroma: the tongue reports bitter and sour, and the nose fills in the several hundred things that make it worth drinking.
Try it yourself
Pinch your nose, take a sip, then let go. The flavour arrives the moment your nose does.