Our Town takes place in a rural setting, in a time far removed from texts and tweets. As a result, the style will strike most modern readers as, well, old-timey. Now, when we say old-timey, we're talking more Andy Griffith than Blazing Saddles. The town of Our Town is a small, rural community in 1930s America, and characters say things like this about it: "Nobody very remarkable ever come out of it, s'far as we know" (I.40).
With a line like this Thornton Wilder accomplishes two things at once. First, we learn that the town is, indeed, a kind of sleepy little village where nothing much happens. Secondly—and this relates to his choice of writing style—we get some authentic small-town dialect. Whoodoggies! (Actually, that's a bit too Southern.) The "s'far," though, lets us know that the Stage Manager, and the other characters, are coming from a rural setting, with a simple (though, as we read on, profound) outlook.
Another part of Wilder's style that helps to convey that outlook comes from the ready references to nature. Of course, living in a rural setting will make nature more important for anyone. That's clearly the case for these characters. Where New Yorkers might experience the natural world by taking a trip to REI, the characters in this play have nature all around them: "No, ma'am, there isn't much culture; but maybe this is the place to tell you that we've got a lot of pleasures of a kind here: we like the sun comin' up over the mountain in the morning and we all notice a good deal about the birds" (I.240).
Again, the writing style and content underscores the importance of the natural world as a source of pleasure for the characters, which is in keeping with the play's broader themes. It may not be a sophisticate hubbub of hipster t-shirts and the latest smartphones, but Grover's Corners is a place where simplicity should not be confused with dullness. As the writing style reflects, these still waters run deep. And you can bet the farm on that.