What exactly are the "ν6 secular Sun-Jupiter-Saturn" and the "1:4 Sun-Jupiter" resonances? In the recent Acta Astronautica article The edge of space: Revisiting the Karman Line, Harvard-Smithsonian Center for Astrophysics astronomer, Space SE contributor and "inverse namesake" of asteroid (4589) McDowell Johnathan C. McDowell lists a number of different boundaries in the solar system in section 3.2. One of them is described as the following:


  The ν6 secular Sun-Jupiter-Saturn resonance which marks the conventional inner edge of the asteroid belt at 2.06 astronomical units (308 million km) from the Sun (26); it coincides with the 1:4 Sun-Jupiter resonance (27) and asteroid orbits near this resonance are unstable, soon perturbed to enter the inner solar system. Although there is no generally agreed definition, this location is a reasonable place to mark as the boundary between the inner and outer solar system.


What (the heck) are the ν6 secular Sun-Jupiter-Saturn and the 1:4 Sun-Jupiter resonances exactly?
The 1:4 (or 4:1) Jupiter resonance is a mean-motion resonance: an asteroid there takes 1/4 as long to orbit the Sun as Jupiter does.
Perturbations by Jupiter at recurring ecliptic longitudes alter the asteroid's orbital period, so asteroids do not remain long in this state.
The Kirkwood gaps in the asteroid belt include this and other mean-motion resonances with Jupiter.

The $\nu_6$ secular resonance (also called $g = g_6$) is more complex: in certain combinations of orbital period and inclination, an asteroid experiences perihelion precession at the same rate as Saturn (the 6th planet) does, resulting in a gradual increase of the asteroid's orbital eccentricity.