I'm quite new and I don't understand everything yet. I was exploring the islands with one of my pets and I walked up to a building, it said that I don't meet the "Hero Requirements" and that I should have "Genetic Power Grade 3" What does that mean? Thanks in advance :)

There are different buildings on the isles, youc an find a list of them here *click*

You found the Cult - if you have the required pet they will give you some items for free :)

Genetic Power means your pets have a bonus in characteristics, it is reached by breeding pets.

For more informations visit the FAQ - under Genetics and breeding questions is a good explanation how you can get GP on your pets.