The purpose of wax is primarily to protect your finish and secondarily to enhance your car's shine. If your car's finish is in good shape, some people argue that wax can't make it any shinier because it just adds a layer on top of the perfectly shiny finish. Other people say that true wax (as opposed to synthetic products) has enough dimensionality that the wax can fill hairline scratches and create a smoother surface which is therefore shinier.
There is also such a blurry line between "wax," "polish," "sealant," "glaze" and other kinds of products that it becomes hard to say whether a car that has a polished finish has any "wax" on it!
Before we go any further, let's define our terms.





Sealant. Sealant normally refers to a synthetic wax-like product that doesn't contain wax.
Glaze. Same as sealant, as far as I can tell. Sometimes seems to imply that it's a sealant that contains some polish (i.e., abrasives).
The Wax vs. Synthetics Debate

The general feeling seems to be that waxes are harder to apply, harder to remove, and don't last as long, but they can produce a rich, warm deep glow that synthetic products can't match. In contrast, most synthetics are easy to put on and take off, and some of them last a long time. They have a much higher melting point than wax, which is helpful on a car's surface which can get pretty hot. They can produce a near-perfect, highly reflective surface, but some feel that the shine lacks depth and is ultimately without "soul." (Some people really take this stuff seriously!) I personally am not convinced. I have gotten a "nice warm glow" from both wax and synthetic products. I think the glow has as much to do with the surface preparation as with the wax.
Some real detailing fanatics apply a bottom synthetic coat for long-lasting protection and then apply a wax top coat for that deep, warm glow. AutoGeeks has a good summary of the debate.