...and a field is just a value that behaves in a particular way. An example outside QFT: phonons [1] behave like particles, but there is no "palpable" sound field, there's only local distribution of implulses of the molecules of air (or whatever medium) where the sound propagates.
Other fields can be seen as attributes of the space itself, and "elementary particles" as wrinkles on it. Gravity is special because it bends the very geometry of space.
> Gravity is special because it bends the very geometry of space.
It's important to remember that this is not true in QFT, and QFT is not true in GR. That is, the math of QFT does not work if spacetime can become curved (at least, if it can become significantly curved).