The 660 km boundary (aka the 660 km discontinuity) is primarily* a mineralogical phase transition in the mid-Mantle. What that means is that the bulk geochemistry above and below this boundary are the same, but the crystalline structures are different (different mineral assemblages are stable at different temperatures and pressures given the same bulk rock chemistry, and the transitions are sharp-ish rather than gradual). The rock below the 660 boundary is maybe 10% more dense than the rock above. Because rock in the mantle is viscous (say, 10^20 Pa s) in the absence of persistent stress or pressure gradients, any topography on this boundary should eventually level out. So seeing kilometers of topography on the boundary means that there are some sort of persistent differences in force in the mantle of magnitude 10-100 MPa that can sustain the gravitational potential energy gradients produced by irregular topography and therefore irregular density distributions. Over broad scales (hundreds to thousands of km laterally) this could be from the big mantle convection cells that drive tectonic plate motion on the Earth's surface. At smaller scales I have no idea what could be driving it.
Another interesting thing about the 660 km (and 410 km and shallower) phase transitions is that I think that the density and viscosity contrasts due to the phase transitions causes a lot of the deep earthquakes such as the Bolivian earthquake from the paper. These earthquakes are in a subducted (sinking, falling if you will) old slab of oceanic crust. As these sink due to density contrasts (they are cold from being at the Earth's surface), they will slow down when they pass through the 410, 660, etc. phase transitions and should deform, kind of like a big icicle that falls of a cliff into water fracturing when it hits the water's surface (except it may continue to sink).
* Some say it's a chemical boundary as well, i.e. that the material above and below doesn't mix. I think most high-resolution seismic imaging of the mantle shows that many convective features such as mantle plumes and subducting oceanic plates penetrate the 660 discontinuity so I don't know if I believe this but it's hard to say and this isn't my area of expertise. It could be either or both although we have solid experimental and theoretical thermodynamic evidence for saying that these are phase transitions.