basically how easily the particle can get through the matter.
if it has charges, then electrostatic forces between the particle and nuclei will slow it down, reducing its energy and hence it won't penetrate as far. this is why neutrons are much better at penetration than say, protons.
also, it depends on the size of the particle. the bigger it is, the more likely it is to collide with something along its path, hence slowing it down, etc. this is why beta particles have higher penetrating power than alpha particles. it is much smaller.
combined, gamma rays have 1) no charge 2) no mass.
therefore, it can never truly be stopped, only some of its energy absorbed.