Wikipedia
A vassal state is any state that is subordinate to another. The vassal in these cases is the ruler, rather than the state itself. Being a vassal most commonly implies providing military assistance to the dominant state when requested to do so; it sometimes implies paying tribute, but a state which does so is better described as a tributary state. In simpler terms the vassal state would have to provide military power to the dominant state. Today, more common terms are puppet state, protectorate or associated state.
Usage examples of "vassal state".
With one stroke of the pen I erased all conquests which might have proved dangerous: not only Mesopotamia, where we could not have maintained ourselves, but Armenia, which was too far away and too removed from our sphere, and which I retained only as a vassal state.
A fragment of it lived on as a vassal state until my father's time, when they revolted and King Shulmanu-asharidu of Asshur destroyed them.
Are we to become a vassal state to Hastur as the price of our freedom?
Latham trusted Rohan more than Hevatia did, but neither of them wished to see Kierst-Isel become little more than the High Prince's vassal state.
Since this was the percentage usually loaned to a vassal state by an overlord, Duke Djai swallowed the tale.
It had been the Princess Arianeira, of all people, who had first mentioned Powell's name to Jaun Akhera as a future ally, once Keltia had been secured as an Imperial vassal state under the Princess's rule.
I declare this village to be a vassal state of the Hittite Empire, subject to our laws.
Under Bayezid, Wallachia became a vassal state which the Turks called Eflak.
You'll be another vassal state of the Empire, yes, but with all your freedoms except the liberty to rob and kill other races.