A protectorate is a faction under the protection of another faction.
Players may choose to request other nations to become their protectorate in the diplomacy screen. Under normal circumstances, a faction cannot ask another faction which is already a protectorate to become a protectorate. However, should the nations be at war, then one nation becoming another's protectorate can be part of the terms of a negotiated peace. No faction can be the protectorate of more than one faction at a time.
Protectorates cede some of their income to their protector nations, in exchange for a pledge from the protector faction to ally itself with it and declare war on enemies invading the protectorate and vice versa. Protectorates also automatically grant indefinite military access to their protector faction. They also have friendlier relations with their protector faction thanks to their status as an ally. The richer a nation is, the more practical it is to make it a protectorate. At the beginning of a campaign, some minor nations are already protectorates of others. If a nation that has protectorates becomes a protectorate, its own protectorates will become protectorates of the new parent nation. For example, if Poland-Lithuania becomes a protectorate of Prussia, Saxony and Courland automatically become Prussian protectorates.
The A.I of Empire: Total War are much more reluctant to break a protectorate agreement than an alliance; protectorates are forced to join a war if they are required by their protecting faction, unlike allies. This makes protectorates much more reliable allies than regular allies.
When a minor nation has suffered great military defeats and/or lost a considerable amount of land, it may offer to become a protectorate rather than face complete destruction. It usually also demands a huge amount of money in return, though, so it is usually a good idea to ignore this proposition unless the invading faction is spread thin militarily.
While simply taking over a region is often more profitable than making the region a protectorate, in some circumstances the trade revenue and tribute paid by the protectorate is greater than the taxed wealth of a region. This is particularly true if the region is small and unproductive to begin with, or if the protector faction has many trade goods and many enlightenment trade technologies researched.