When a minor nation has been attacked by another 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 a great power. However, the benefits of intervention are significant. You immediately acquire the minor nation as a colony. You have control over all their armed forces and can deploy more regiments to defend their provinces.