Buffs are bonuses that are applied to either your empire or to an individual nation.
When a buff is applied to the empire, all nations within the empire will benefit from that buff. If the buff is applied to a single nation, than only that nation will gain the benefit.
To view the buffs that your empire currently has, you will need to select the empire buffs option from the Empire Action Menu
To view the buffs that a nation currently has that are not provided by the empire, you will need to select the nation buffs option from the Nation Action Menu
The most common way for your empire to gain a buff is to an inventory item that applies a buff.
A team buff is gained if your team controls a tower, and/or a wonder. A team buff is applied to all empires in the world that are on the same team. Team buffs generally last for 1 hour. The strength of a team buff is based on an empire's team loyalty. So if an empire has 50 points of loyalty on a team, that empire will only benefit from 50% of the buff.
All buffs will have an expiration time and once the buff timer has expired, the buff will be lost.
Buffs do stack. So if you have two buffs with the same effect, the system will add them together before apply the effect.