This is one of a series of glass Klein bottles made by Alan Bennett in Bedford, United Kingdom for the Science Museum, London. It consists of three Klein bottles, one inside another. A Klein bottle is a surface which has no edges, no outside or inside and cannot properly be constructed in three dimensions. In the series Alan Bennett made Klein bottles analogous to Mobius strips with odd numbers of twists greater than one.
I disagree that it “cannot properly be constructed in three dimensions” as it obviously has been. Perhaps they meant defined…
[Image and description from here, via somewhere else.]
[UPDATE: Here’s a visual summary of a single Klein Bottle, showing its relationship with a Mobius Strip (thanks to Strider).]