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The monsters are real. They were relatively free-willed back in Egyptian times, except they were bound to tablets and could be summoned at will. Nowadays, through technology, they're bound to the computers, and 'summoned' in incorporeal forms as 'holograms'.
When duelers take place in duels they connect with these holographs and they can effect them, hence lifepoints actually taking a toll on the duelists.
Egyptian God cards are particularly strong, and as such they're far less bound by the computers and are less of a hologram.