A tributary state is a state that is subordinate to a more powerful neighbour. It was a form of subordination in pre-modern times.
The tributary sent a regular token of submission to the superior power. This was a tribute, a substantial gift of wealth, such as the gold, produce, or slaves. The tribute might best be seen as the payment of protection money. But there were other ways to show submission as well.
For modern forms of state subordination, see puppet state, satellite state and client state.