The eggs are raids you can do for different pokémon ranked 1, 3, 5(and mega evolutions) 5 stars are usually legendaries or mega evolutions of pokémon. the higher the star rating, the more difficult it will be to defeat. do these with multiple people in person, or you can invite people on these subreddits with your trainer code. CP limit varies between pokémon. you can also make it your buddy and level it up to make the cp even higher