I also use CPL to shoot through glass.
What's cool about a CPL is that it can selectively decide what light can pass through the filter based on each waves polarity. Light reflections off a surface will generally all have (mostly) the same polarity whereas ambient light will have random polarity. What that means is CPLs are particularly adept at removing "reflection" ... ANY kind of reflection.
The reason leafy green foliage looks "greener" through a CPL is because leaves have a waxy coating that reflects light... giving them a bit of a shine (even leaves that you wouldn't normally think of as shiny have this coating.) By eliminating the reflection off the leaf, what you see is the true green of the leaf itself rather than the reflection of the bright sky. This is something you CANNOT correct in Photoshop (not unless you plan to clone in leaves from someplace else.) The ability to cancel out reflections in the air, on walls, on glass surfaces, on waxy surfaces, on water, in foliage, etc. means the CPL just generally creates superior contrast and makes colors look more vibrant -- but not because you cranked the saturation, but really because you eliminated reflections from all those surfaces which were muting the colors.
Not all CPLs are created equal. Low cost CPLs may create a color-cast in your images and may not reduce as much glare as a high quality CPL. If you've got a polarized monitor (a lot of monitors have polarized surfaces) you can hold the CPL in front of it and rotate it slowly. Make sure the side that mounts to the camera faces YOU (yes... it matters. Just for fun, flip it around backwards and do the same thing and you'll see the result is COMPLETELY different.) A good CPL will take the image almost completely black at some point. A budget CPL will just dim the image but it wont go nearly black. BTW, use the filter backward and you'll notice that instead of being color neutral... the image shifts between a gold/amber color and a blue/violet color (you can actually "buy" blue/gold polarizers to create interesting polarization effects in photos and they're just normal polarizers with the filter installed backwards.)
Sometimes a hint of reflection is a good thing... so depending on what I'm shooting, I might find the optimum tuning for the CPL, but the deliberately de-tune it slightly. This way I don't completely eliminate reflection (which wont look as realistic), but it allows me to show off a hint of it without the reflections being distracting.
Every photographer should own a CPL and at least one ND filter.