Retrohaling is the technique of exhaling a portion of cigar smoke through the nose rather than the mouth. The smoke passes through the retronasal passage that connects the back of the mouth to the nasal cavity, where it encounters the olfactory receptors that perform most of what we call “tasting.”
The biology is the reason. The tongue identifies five basic tastes (sweet, salty, bitter, sour, umami). The roughly four hundred olfactory receptors in the nose identify thousands of distinct aromas. When you eat a strawberry, the sweetness and the slight tang come from the tongue, but the unmistakable strawberry-ness comes from the nose. The same is true of cigar smoke. Without the retrohale, you are tasting fifteen percent of what the cigar is doing; with it, you are tasting most of it.
The technique takes practice. Draw smoke into your mouth as usual. Close your mouth and gently push a small portion of the smoke up and out through your nose, almost as if you were yawning with your mouth closed. Do not blow hard; a small amount of smoke produces the full effect. New smokers often cough or feel a sharp note on the first few attempts; this is normal and fades quickly with practice.
The first cigar where you retrohale properly will reveal flavours you did not know the cigar contained. The second cigar will feel pale by comparison if you forget to retrohale.
For more on cigar fundamentals, see The Anatomy of a Cigar.