Throw a stone into a pond — ripples spread out, changing the scale of the wave. The new theory works much the same way: it gives each particle its own "scale ripple," and it's this curvature of an invisible space that turns out to be the source of mass.
The authors started with gravity, but not the usual Einsteinian kind — rather its extension, Weyl geometry, where the very notion of length can vary from point to point. Into this geometry they embedded all the known fields of the Standard Model: quarks, electrons, and the carriers of the weak and electromagnetic interactions. The key trick is a special quadratic construction, like a stretched sheet with a dimple in the middle: it allows you to single out a scale particle (the weylon) independently of the Higgs boson.
When scale symmetry is spontaneously broken, like a pencil balanced on its tip falling in a particular direction, the quadratic curvature turns into ordinary Einsteinian gravity with a cosmological constant (the very one that's pushing the universe apart). At the same time, mass emerges for the weylon and, surprise, a potential for the Higgs field, which would otherwise be forbidden by symmetry. In this way, the mechanism for generating mass for all particles becomes unified: the weylon, the Higgs, and Yukawa couplings work together.
Finally, the theory predicts new interactions between the Higgs and the weylon that could be searched for at colliders. The stone has been thrown, the ripples are still spreading.
Weyl geometry was proposed almost a hundred years ago, but Einstein himself rejected it due to inconsistencies with atomic clocks. Today it's making a comeback in a quantum version.
In Peter Watts's novel Blindsight, aliens manipulate the laws of physics themselves — the new theory takes a first step toward understanding how that might work.