Eggs do need to be refrigerated for safety.
When you buy store bought eggs that have already been refrigerated they should always remain refrigerated until they are consumed.
The eggs that are farm fresh eggs or eggs that come from your own chickens do not need refrigerated as long as you plan to eat them the same day or within a week of gathering the eggs.
Eggs should be consumed within 1 to 2 weeks of purchasing them because eggs that are kept longer than a few weeks can go bad.
If an egg is bad it will smell bad when cracked open and if so you should throw it out.
I always keep my eggs refrigerated until I'm ready to eat them.