Many Nations likely fall into one of these two categories:
A) You are in a strong Nation, and you can (and want to) protect yourself and others, OR
B) You are in a smaller, more peaceful Nation, and you'd prefer to avoid War altogether.
If one of those applies to your Nation, then a Vassalship agreement is for you! Overlord-Vassal relationships last for a set amount of time (determined in the Treaty Proposal) and a certain set of changes happen when this relationship goes into effect:
For Overlords, things don't change too much. The only real change is the knowledge that you're now officially protecting another Nation - which means if your Vassal makes enemies, or had prior enemies, those enemies will likely be coming after you now! Beyond that, mechanically, nothing else changes for the Overlord.
For Vassals, things change a bit more. Vassals cannot make or receive diplomatic Proposals from/with other Nations. This means War can't be declared on you, and you can't declare War on others - nor can you capture Relics or take part in Sieges. However, if your Overlord is at War, your Nation members can be killed once per day in the wilds by your Overlord's enemies. Being a Vassal means temporarily giving up diplomatic power in exchange for protection, so choose carefully when becoming a Vassal!