From Civilization V Wiki
Wonders are the spectacular buildings, inventions, and concepts that have stood the test of time and changed the world forever. Wonders require much time, energy and effort to complete, but once constructed they provide your civilization with many benefits.
There are two types of wonders: World Wonders and National Wonders.
World Wonders are unique; only one of each can be constructed during a game. (For example, the Great Lighthouse is a World Wonder; whichever civilization completes its first is the only one who can build it.) Great Wonders tend to be extremely powerful and extremely expensive, as well.
Losing the Construction Race
If another civilization completes a Great Wonder while you are in the process of building it, your construction ceases and a certain amount of your production efforts are converted into gold. (This doesn't occur with National Wonders, since each civ can have its own version of a National Wonder.)
National Wonders may be built once by each civilization in the game. That is, each civilization can have its own National Epic Wonder (though no civilization can have two of them).
List of Wonders
All the Wonders in the game are organized below by category:
Effects of Wonders
A Wonder can have a huge variety of effects. One might greatly increase a city's productivity, while another might increase your civilization's happiness. A third might increase your civilization's output of Great People, and a fourth might increase the defensive strength of all of your cities.
If you capture a city, you will capture all World Wonders constructed in it. All National Wonders are destroyed, however.