A forager that has found rich forage performs a figure-of-eight circuit on the comb, and the informative part is the straight waggle run in the middle. In the darkness of the hive she cannot see the sun, so she substitutes gravity for it: straight up on the comb stands for the sun's direction, and the deviation of her run from vertical reproduces the angle between the sun and the flowers.
Duration carries distance. Longer waggle runs indicate more distant forage, though the exact seconds-per-metre relationship differs between honey bee species and even between populations, so a dance is read against the local dialect rather than a universal scale. Followers press against the dancer, pick up the vibrations and the odour she carries, and depart.
Karl von Frisch published the decoding in the mid-twentieth century and shared a Nobel Prize for it in 1973. What is often overstated is precision: recruits do not fly to an exact point. Many arrive in the broad neighbourhood and then search on scent, and a substantial fraction of dance followers never locate the advertised patch at all.