By definition, realism (in literature) depicts the literary situation as something in its true to life representation. What this means is that the setting and characters make sense to the reader as a place which can be readily identified as true to life. The setting is realistic to the place being described. Characters are readily identifiable and acceptable as being realistic. The clothing, customs, setting, and dialect all speak to realism.
As for Synge's play, he himself openly states that the "phrases [he] employ[s] [he has] heard also from herds and fishermen along the coast from Kerry to Mayo, or from beggar-women and ballad-singers nearer Dublin" (Preface). He goes on to state, "On the stage one must have reality." Synge embraces realism and ensures that his play speaks in realistic ways to his native (and not so native) audiences.
The stage props and setting are not elevated or heightened in any way. The characters are typical townfolk with typical problems (at least to the typical Irish man or woman). The plot is recognizable as something that an ordinary person would (or could) go through. The dialect contains diction (language-specific terminology and slang) which speaks to the recognizable aspects of the Irish language (using a mixture of English, Irish, and Gaelic).