Take an ordinary steel spring and imagine that it is floating in space. Attach identical springs to the ends of that spring and more springs to the ends of those until a grid lattice of steel springs is constructed that pervades all of three-dimensional space. This is the 3-D mattress. This entire lattice of springs represents a quantum field in our analogy. Let's suppose it is the electron field. If a single spring in the lattice is plucked, it will vibrate, and this vibration corresponds to the quantum, an electron associated with the field. Two springs far apart on the lattice could also be separately plucked and the resulting vibrations would correspond to two quanta, two electrons at those points.
We could imagine a second mattress made of a different kind of spring, maybe a heavier one, that is superimposed on the first lattice, and this mattress would represent a quark field. Its vibrations correspond to quark particles. So for each field there is a different mattress of springs pervading all of space, and the vibrations of a specific spring correspond to a particle at that pint.
So far these different superimposed lattices of springs representing all the fields of nature are supposed not to touch each other. But now imagine that the various lattices of springs representing quarks and leptons can get linked together by another set of springs, which represent the gluons. The electron lattice is linked to the photon lattice and this to the quark lattice and so on. This space of connected spring lattices now represents an interacting quantum field theory.
If one of the springs of the electron field lattice has a vibration corresponding to an electron at some point, this vibration can be transferred to the photon field lattice. That now starts vibrating corresponding to photons in the neighborhood of the electron. The photon could also couple to the quark, and so on. All fields--lattices of different kinds of springs, one for each particle--can interact with each other via some third kind of field.
To press this analogy even further, we imagine that the springs are invisible. All that remains of the lattice of springs is its set of vibrations. Further, the individual springs should be made infinitely small so that even in a tiny region of space there are infinitely many springs. This super 3-D mattress of tiny invisible springs is rather close to what theoretical physicists describe as a quantum field. All that remains of the field is its potential vibrations at each point--the quanta manifested as various particles. These particles can move about in space and intersect with one another. The underlying reality is the set of fields, but its manifestation is the particles. The universe is a great spawning ground and battle field of the quanta, according to relativistic quantum field theory.
With this background we can now list the central dogmas of relativistic quantum field theory:

1. The essential material reality is a set of fields.

2. The fields obey the principles of special relativity and quantum theory.

3. The intensity of a field at a point gives the probability for finding its associated quanta--the fundamental particles that are observed by experimentalists.

4. The fields interact and imply interactions of their associated quanta. These interactions are mediated by quanta themselves.

5. There isn't anything else.