When an Old World  Neutral State has been attacked by a Great Power its leaders often seek a friendly Great Power to declare war on their enemy and protect their nation. This action by a Great Power is called intervention.

You receive offers to intervene only if you are the Great Power with the best relationship to the attacked Minor Nation and only from a Minor Nation in which you have an embassy.

If you accept the offer to intervene, you pay all normal penalties for declaring war on the Great Power. However, the benefits of intervention are significant. You immediately acquire the Minor Nation as a colony. You gain control over all their armed forces and can deploy more regiments to defend their provinces. 

You will not receive offers to intervene from tribes in the New World, even if your country is very friendly with them because Great Powers simply attack tribes, they do not declare war first. The only way to protect a tribe from other Great powers is to use a merchant unit and purchase land in all of the provinces of the tribe.  In order for another Great Power to attack a New World province in which your country owns land, the aggressor must first declare war on you. It is never necessary to declare war on a tribe.