I think Marinatos is right when he argues that the labrys became associated with a Minoan solar Goddess and the rising of the sun. He is persuasive in linking the simple symbol with other such Near Eastern glyphs, like the ankh or the ox head or the flowering lotus. This would make sense as a very localized expression of a iconographic practice happening all over the Anatolian sub-stratum koine in this time period (see here). I am also a fan of the notion that the glyph was originally simply a representation of the tool, either for war or carpentry, both of which carry with them a certain power (of destruction or creation). The basic double-axe glyph is found all over the place, even in Neolithic Europe, and I think it only comes to have power as a particularly "religious" symbol in the Minoan civilization, for whatever reason.

There is a lot of modern nonsense about "Minoan paganism" and symbology and such on the internet today, and it can be hard to separate the junk from the good stuff. While I don't agree with 100% everything in this book, Marinatos Minoan Kingship and the Solar Goddess (2010) is pretty darn good on the Minoans, and is cutting edge as far as new theories about their identity and the interpretation of some of their more enigmatic features.