What is a graviton?
If the theory of gravity is fundamentally of a quantum nature, the graviton is the particle whose exchange between two masses is responsible for the gravitational force:
To understand this, one has to remember the traditional field/particle association that one encounters in quantum physics: a photon is at the same time a particle and an electromagnetic field (in fact an electromagnetic field is usually a superposition of many photons). The Higgs is a particle that is detected at CERN but it is also a field that is present everywhere and gives mass to the other particles.
Similarly, if the theory of gravity is a quantum theory, the graviton is a particle but also a gravitational field. On the field side, it can be seen as a field of deformation of space-time. On the particle side, it is the particle whose exchange leads to the gravitational force.
Now, the theory of general relativity as proposed by Einstein is not a quantum theory. So, the graviton is, in the strict sense, not part of this theory. But most theorists believe that eventually there will be a quantum generalisation of general relativity. In this context, there will be a graviton, and, even though we do not know this theory yet, because we know well the gravitational force, we can infer from it a certain number of properties of the graviton: for example, it has zero mass and travels at the speed of light.
If it turned out that gravity is not a quantum theory (a possibility not favoured today because it leaves many questions unanswered), then only the field interpretation is valid, not the particle interpretation, and there is no graviton.