The “Legendary” eggs are the Thunder/Magma/Icicle eggs. You can see what the eggs look like and what their “catch phrases” are here.
If you have an adult of all three of those breeds (and are able to pick up from the cave/AP – meaning no more than 3 eggs and/or 3 hatchlings) there is a Breed-Specific Action they can perform once every two weeks called “Summon”. If…and it’s a big if…you succeed you get a special egg/dragon (that’s like the “giving” holidays – Christmas/Valentines – in that you can only have two on your scroll). If you give one away, you can continue to summon until you keep two, then the action disappears forever.