A "Konstantinato" is an ancient Byzantine coin first minted by the emperor Constantine in an attempt to bring economic order to an almost bankrupt Roman Empire.
The real innovation behind the coin was two-fold: First; it was one of the very first monetary units to be made of real gold at a specified weight that was backed by the issuing authority. Second; it featured the cross in such a way as to make the emperor's intentions towards the religion unmistakable.
These coins would be circulated around the empire with an unmistakable message; "a new religion was being adopted".
Reproduced Konstantinata are currently used in Eastern traditions as a sort of good luck charms. They are most commonly used as protective gifts for newborns that haven't been baptized yet, but I remember Gerochristo putting one under the floormat of a car I had just bought (actually it was a 2 Euro coin), in that case the same meaning was implied (good luck / good fortune). Martirika and Filakta are essentially variations of the same intention. They may or may not represent a coin, but serve the same protective purchase (our "boy" and "girl" bracelets for instance).
A word to the wise because we hear this a lot: If you ever come across an actual gold coin from antiquity ... avoid it like the plaque! The ones for sale on the internet (and elsewhere) are most likely reproductions - the people selling them are either uneducated or just plain thieves. If you did buy a fake one count your blessings ... because to trade in genuine antiquities is illegal in most countries. You also don't want to claim to have found it ... that's almost worse than being arrested! You'll be filling out paperwork from the host country and the European Union for years, and in the end the coin will not be yours.
I was actually told by one of my jewelers that the best thing you can do if you see one is to just walk away and act like you never saw it ... "they are cursed".