Monopsony is a market structure in which there is only one buyer of a good or service. If there is only one customer for a certain good, that customer has monopsony power in the market for that good. Monopsony is analogous to monopoly, but monopsony has market power on the demand side rather than on the supply side.
A common theoretical implication is that the price of the good is pushed down near the cost of production. The price is not predicted to go to zero because if it went below where the suppliers are willing to produce, they won't produce.
Market power is a continuum from perfectly competitive to monopsony and there is an extensive practice/industry/science of measuring the degree of market power.
As an example, for workers in an isolated company town, created by and dominated by one employer, that employer is a monopsonist for some kinds of employment. For some kinds of U.S. medical care, the government program Medicare is a monopsony.