What exactly are the "ν6 secular Sun-Jupiter-Saturn" and the "1:4 Sun-Jupiter" resonances?
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.