As the game progresses from era to era your civilization can enter a Golden Age or a Dark Age. If you're doing better then the other civilizations or completing many Historic Moments, then there is a good chance you will enter a Golden Age in the next era. If you start falling behind, you might fall into a Dark Age.
A Golden Age is a time of great prosperity for your people. Your Loyalty decays at a slower rate than normal. Not only are your cities more likely to stay in your civilization, but you might even convert nearby cities into your civilization as well. In addition, you can choose a Dedication for the next era. Dedications are powerful bonuses that apply to a specific part of your civilization. But be aware that earning a Golden Age makes it harder to earn the next Golden Age, and easier to fall into a Dark Age.
Dark Ages are difficult periods of time for your people. Your Loyalty decays faster then normal, which may lead to the cities at the edge of your civilization leaving and becoming independent cities, or being conquered by other players and integrated into their civilization. You can prevent this by using your Governors, or by strategically choosing to lose cities (and maybe hope to reconquer them later.)
Don't worry or be too upset if you fall into a Dark Age because you have the chance to enter a Heroic Age. Your threshold for entering a Golden Age will be lower if you're in a Dark Age, and if you pass that Golden Age threshold, you will enter a Heroic Age. A Heroic Age lets you choose three Dedications in the next era! This may actually set you ahead of a player who goes from a Golden Age to Golden Age, if you're able to take advantage of your abilities.
If you exceed the Era Score threshold for a Dark Age, but do not have a high enough score to enter a Golden Age, then you enter into a Normal Age. During a Normal Age you may still choose a Dedication for that age, but you don't not gain any other bonuses or penalties.
'Dark Ages also give you acces to special Dark Age Policies. These wildcard policies can provide you with options to emerge from a Dark Age, but carry a cost. For example, the Isolationism Policy gives bonuses to internal Trade Routes, but prevents you from building or buying Settlers or settling new citites.
You may complete Dedications during a Normal and Dark Age to increase your Era Score, giving you a better chance to gain a Golden Age in the future.