Laocoön was the priest of Poseidon at Troy who was killed, together with his two young sons, by two huge sea-serpents who crushed all three in their coils. (The scene is portrayed in the famous Greek statue that stands in the Vatican Museum.)
There was another Laocoön who was the son (or possibly the brother) of Oeneus, king of Calydon. The name, however, does not appear to relate to the serpentine fate, and it perhaps derives from laos, 'people' and some such word as coinos, 'common', meaning 'impartial to people', 'common to all the people'. If so, it is a generally commendatory name.