In a particle physics context I've heard this phrase used. I guess it means that the mass of a particle is less than you'd naively expect from $E=mc^2$ after computing the momentum uncertainty corresponding to some appropriate length scale. Assuming my interpretation of the phrase is right, how does a symmetry let you get away with a smaller mass ?
Answer
It means protection from radiative corrections. If you integrate loop corrections to the mass, out to some virtual momentum scale $\Lambda$, for a generic Lagrangian you would get contributions of order that scale. So what if you observe $m<<\Lambda$? Well if there is a symmetry in the theory than guarantees that perturbative corrections to the mass will vanish, then you say the mass is protected by the symmetry, problem solved. Otherwise you've got explaining to do why $m<<\Lambda$.
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