The term given to the body with the pre-eminent gravitational influence over a system of other bodies. The term has general application at a variety of scales so, for example, Jupiter is the primary for its extensive system of moons, while the Sun is the primary around which Jupiter (and all the other planets of the Solar System) pursue their orbits.
Defining the primary body of a system is related to the concept of the barycentre, the point that marks the centre of gravity between two objects. For any two bodies, the barycentre will lie closer to the more massive of the pair, and where the discrepancy is very large, it will actually fall inside the volume of the more massive primary body. This is the case with the Sun and all the planets of the Solar System, for example, and is also commonly seen for systems of moons orbiting around a planet.
Defining a system's primary becomes more difficult where two bodies are closer to one another in relative mass, in which case their barycentre lies in the space between them and they follow a mutual orbit. One example of this situation is the case of Pluto and its moon Charon. Charon is massive enough relative to Pluto that their barycentre lies between the planet and the moon, and for this reason the pair of bodies are sometimes referred to as a 'double planet'.
At least in Pluto's case, the planet has about eight times the mass of Charon, and is there relatively easy to define as the primary body of the Plutonian system. Matters are rather less clear in the case of binary stars with nearly equivalent masses. In these situations, the two (or more) stars will orbit around a common centre of gravity, and it consequently becomes rather less useful to define the marginally more massive star as the 'primary' of the system.
The word 'primary' can be used either as an adjective or a noun, so it is meaningful to speak of, for example, the 'primary star' of a stellar system, or simply that system's 'primary'. The latter usage tends to be more common, especially in situations where the intended object is clear from its context.