The Andy Griffith Show (1960)

Answer: As noted in the previous answers, in real life, things like this provided wind and/or rain deflection, and also maintained a bit of privacy when blinds were raised somewhat. The interior courthouse set was located in the studio, so the "outside" Main Street didn't exist. I believe these things were added to the courthouse windows for practicality, to avoid some crew movement being visible on the opposite side of those windows. These are not "window boxes" to hold anything, as they're actually bottomless; we can see the Venetian blind's long pull cords under them. They're made of plywood and simple to build, so the "material and labor" was inexpensive. Similar variations made of different materials are in other movies/shows. In 1957's "12 Angry Men," textured chicken wire glass panels are in the jury room windows, and in "Jesse Stone: Night Passage" another type is in Jesse's office windows.

Super Grover ★

Answer: Those "boxes" are valences that used to be very common, before air conditioning. They allow for windows to be open during rain storms. They permit air circulation, without letting the rain in.

Answer: I suspect these were common, as to block the wind from blowing the blinds and papers on the desk.