In 3rd person when you look underneath the players feet, there are holes were their feet should be that allow you to see the outside world.
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You are seeing that because the camera has gone through the texture of the bottom of the feet.
You are looking "Inside" of the legs.
Xavier is right.
When you look from below at another player standing on glass blocks, you don't see holes, you see the texture of the "leg bottom".
See http://www.minecraftwiki.net/wiki/Skin for the layout of the skin file.
As far as I know, that's not a glitch (and if so, a very old one) and has been there since whenever f5 became available.