This command will spawn a fertilized egg for the type of dino that your crosshair is over (i.e. targeting a Parasaur will result in a Parasaur egg). The dino you target will become aggressive towards you if you pick up the egg.
Find below information relating to the GetEgg command in Ark.
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This the only way to use the GetEgg console command. After running this command, an egg for the same species of dinosaur that your crosshair is over (target) will be spawned.