After the comic eavesdropping scenes, the play becomes serious with Don John's villainy at work. And with Benedick and Beatrice momentarily experiencing a loss of wit (and, thereby, experiencing an inability to provide comic dialogue), Shakespeare introduces another character to provide comic relief and to keep up the humorous mood of the play. That character is Dogberry.
Dogberry is the town constable. A constable was like a sheriff or police officer. He is in charge of keeping order in the town. His partner is another comic character named Verges, and serving under them are several watchmen (town guards). The characters of Dogberry and Verges are burlesque or comic portrayals of the actual town constables of Shakespeare's time. Many of these constables, apparently, were not very competent in their jobs. Some may have been entirely ineffective. Thus, the audience would find these characters all the more amusing because they would be aware that, despite the comic exaggeration of these two characters, their ineffectiveness was a true feature of many real constables.
Dogberry and Verges' ineffectiveness as constables is underscored by their linguistic ineffectiveness. Shakespeare provides a great deal of verbal humor by frequently having these characters say the opposite of what they mean. Verges, for example, says "salvation" when he means damnation (in line 2), and Dogberry says "allegiance" (loyalty) when he means disloyalty (in line 5). Such linguistic muddles persist throughout all of their dialogue. The lines are humorous, but they also reveal the incompetence of the characters.
In this first scene involving Dogberry, he and Verges instruct the watchmen how to respond to any disturbances at night. For example, if the watchmen meet any disorderly drunks, they are to tell them to get to bed (lines 39-40). But Dogberry advises the following if the drunks refuse to go to bed:
Let them alone till they are sober. (42)
In essence, then, Dogberry is telling his men to do nothing. For any problem that might occur during the night, Dogberry's advice is the same: just let it pass, do nothing. The humor in this, of course, is that is just what many real constables did during the Renaissance: nothing. Fortunately, the watchmen are not listening to Dogberry or do not understand what he is saying. For later in this same scene, they do something: they arrest two suspicious men.