Yes eggs do really eventually expire and go bad even when kept properly refrigerated so be sure to eat the eggs before they can go bad.
Eggs will usually last for up to 5 weeks in the refrigerator before going bad so as long as you eat the eggs within 5 weeks they can still be good to eat.
I've heard of people freezing eggs too which makes them last longer but the eggs won't be as fresh in the freezer and the shells will likely crack as a result.
I usually use eggs within a week or two so it's usually not a problem of them going bad.
Even when eggs are past the expiration date by a little the eggs are still safe to eat as long as you keep them refrigerated.
You can test to see if the eggs are still good by doing a floating egg test.
Fill a bowl with water and place the egg in the water and if the egg floats the egg is bad.
If the egg sinks to the bottom the egg is good and safe to eat but if the egg sinks to the bottom but stands up on one end the egg is still good but not as fresh.