The game tracks individual relations between each country, which may run hot or cold. You can initiate Treaties between nations, do things to make them more friendly toward you, or provoke them to anger.
Naturally, part of the Diplomatic aspect comes into play when you have made another country really angry, or you’re really angry at them! You can declare war, and call in your allies to help you. Later, you can try to negotiate peace — hopefully one that will work in your favor, and meet your war aims.
Victoria uses a “Casus Belli” system — you should really have a good excuse to go to war. If you don’t, your reputation as a respectable country will go down, and it’s not just other countries. Your own people will wonder what you were thinking, too! But there are plenty of reasons why you might have a valid excuse to go to war, short of sheer boredom at the palace. You could want land you think is rightfully yours, or they may have done something nasty to you and you want to get them back.
Along with the Casus Belli system is a related War Aims system. If you have a rival for leadership of the different German countries and city-states, for instance, you might choose to fight them for influence. You go to war, citing interference with your clear interests, and beat them in battle. Then you make a peace offer making them give up a country in their Sphere of Influence. Then that country will follow your direction in foreign policy, instead of your rival’s. If you don’t do so well in the war, you may fail to achieve your war aims, which means you may lose prestige in the eyes of the world, and may lose your Sphere of Influence.
That’s another part of the Diplomatic system — Great Powers, Second Tier Powers, and Spheres of Influence. The eight most powerful countries in the world are considered Great Powers, which gives them special abilities, including the ability to collect “Spheres of Interest” — a degree of influence over what decisions other countries make, either because they like you a lot, or they fear you a lot. The next eight most powerful countries are considered Second Tier Powers, and they may try to “knock off” the Great Powers so they can take their place. Otherwise they may be doomed to remaining in the shadow of a Great Power, as part of their Sphere of Influence.
There are even underhanded things you can do behind the scenes, like ruining the reputation of another country, and convincing other countries not like them. Of course, they can be doing this to you, too.
All in all, the complex Diplomatic functions you have at your disposal create a varied and interesting pattern of relations around the world, through both war and peace. If you play your Diplomatic efforts correctly, this is how you can rise to Great Power status.