In the first chapter, Frank Bryce, the unfortunate gardener for the Riddle house, is arrested for the murder of the Riddle family in Little Hangleton, England. Frank is soon released because there's zero physical evidence to show how the Riddles were murdered. Although Frank claims to have seen a teenage boy murder the Riddles, no one believes him. In fact, the villagers are absolutely against Frank. Even though no one officially accuses him of anything, everyone seems to agree with village resident Dot when she comments, "So far as I'm concerned, he killed them, and I don't care what the police say" (1.23). So Frank has been convicted of murder according to public opinion, even if there's no real evidence against him.
This is why we find the name of the village pub, the Hanged Man, to be significant. A hanged man is (generally) a man who has been convicted and executed of a crime. It's in the Hanged Man pub where all of these unfounded rumors against Frank Bryce start circulating, so the name of this pub foreshadows what Frank Bryce is. Oh, he hasn't been executed (at least, not until later on in Chapter 1), but he has definitely been convicted, if only unofficially in the minds of all the villagers.