What exactly is a pomeron?

Before the quark model became the standard model for particle physics, the prevailing model for elementary particle scattering was using the theory of Regge poles.

At the time (1960s) electromagnetic interactions/scatterings could be described very well with Feynman diagrams, exchanging virtual photons. The study of strong interactions tried to reproduce this successful use of Feynman diagrams ; for example there was the vector meson dominance model :

In particular, the hadronic components of the physical photon consist of the lightest vector mesons, ρ , ω and ϕ . Therefore, interactions between photons and hadronic matter occur by the exchange of a hadron between the dressed photon and the hadronic target.

The Regge pole theory used the complex plane and Regge trajectories to fit scattering crossections, the poles corresponding to resonances with specific spins at the mass of the resonance but arbitrary ones off. The exchange of Regge poles ( instead of single particles) was fitted to scattering crossection data. See this plot for some of the "fits" .

At the time , when it seemed that the Regge pole model would be the model for hadronic interactions, it was necessary to include elastic scattering, i.e. when nothing happened except some energy exchanges. The Regge trajectory used for that was called the Pomeron trajectory.

the particles on this trajectory have the quantum numbers of the vacuum.

If you really want to delve into the subject here is a reference. With the successes of the standard model the Regge theory was no longer mainstream, but considered old fashioned.

This abstract for , The Pomeron and Gauge/String Duality is revisiting the pomeron .

The emergence of string theories though revived the interest in regge theory and particularly the veneziano model which describes the regge poles and considers the resonances as excitations of a string.

OK, here is the OP's requested side-supplement to @anna 's mainstream answer. Even though the OP's request is really a history of science one, I am not reluctant to post it here, as it is not just about the pendulum of fashion in the strong interactions (only now used indistinguishably with "QCD", after the latter's acceptance).

The reason you don't see discussions of "soft at heart" physics in QFT books now is because only few people, or else, or else, are working on "high s, low t" physics today.

So, diffraction is well-described by the exchange of some ripple of the strong vacuum, a collective excitation of QCD, most believe, the Pomeron; but, basically, people look away and relegate such to the outer edges of their mental map, like "hic sunt dracones" in renaissance maps... The closest you'd get to your proverbial "modern source" might be E. Levin's course... Chapter 2, "The Great Theorems" is a "must" summary. It is alive and well, but out of focus, and nothing else in QCD, or elsewhere, can supplant its utility.

In case you never noticed, in 1964, the year Gell-Mann wrote his 2-page quark paper (item 12), the bulk of his research and publications was on vacuum trajectories and Regge theory. This was hardly a symptom of a collective community delusion or wrong-mindedness! It's just that soft physics is hard to do. The community moved away and only the old-guard creative Russian physicists stayed in.

What actually happened is that, in the 70s and early 80s, discovering new particles and confirming short distance QCD (hard scattering, the confirmation of the tri-linear gluon coupling, quarkonia,...) revolutionized the focus of the strong interactions, and people started doing "clean" parton scattering experiments instead of messy triple-pomeron-coupling determination ones.

Lattice gauge theory does handle soft (~collective multigluon) physics, but it is best suited for hadronic spectra, matrix elements, and even illustrating the roiling of topological excitations such as instantons in the vacuum. But I don't know of any contributions of it to diffractive physics. (It hasn't even delivered on Wilson's promises to derive the effective low energy σ-model of chiral symmetry breaking out of the fundamental QCD Lagrangian.)

So the answer to your questions "why?" is because its just too hard, and harder to make trenchant experimental predictions with it, to warrant great experimental effort. The QCD vacuum is the classic hic sunt dracones area, real and important as it might be... But, hey!, isn't confinement, as well?