Eggshells are good for compost and can add needed calcium to the compost pile which makes for better compost.
However the eggshells do not break down as fast as other foods that you compost but the eggshells are good and perfectly fine to put into your compost pile.
When putting the eggshells into the compost you should crush them down as fine as you can get them to help the eggshells break down in the compost soil faster.
The calcium in the eggshells is an important nutrient to help plant cells build walls.