Dragon Eggs
Illyrio gave Danny the three dragon eggs because nothing happenned to them while fAegon lived with him.
Think about it, you are Illyrio Mopatis and you put a dragon egg at fAegon's craddle following this old Targ tradition hoping this kid will make this eggs hatch, no matter how old they are. Months pass by, then years and the dragon eggs don't hatch. The boy loses his interest in them and you, Illyrio Mopatis, come to the conclusion that they are too old. If there was ever a dragon in there, it died a long time ago. Now they are nothing but a relich.
Your life goes on and, as fAegon leaves your side with JonCon, you no longer think about them, maybe they remind you too much of the boy and it makes you sad.
Then one day the last two legitimate Targaryens appear at you door, your merchant mind sees a possible bargain to be made with this two kids. You arrange a marriage with the girl and the Dothraki. She requires a wedding present and while she stays at your house the dragon eggs come back to your mind. They are useless but the girl (and the brother) would consider this useless eggs the biggest present they could ever get, considering their dreams of conquering the Seven Kingdoms back. So you give them as a present. They will never hatch. The eggs are useless, except they aren't.
Surprisingly, they dragons are born. Magic. You made a mistake but you couldn't have seen it coming. That's why Illyrio gave the three eggs to Danny, because fAegon had them for a while and nothing ever happenned.
