Heat capacity C (or specific heat capacity s) are a measure of reluctance of a substance in changing its temperature.
A good conductor of heat has less value of specific heat capacity. An insulator of heat has high value of specific heat capacity.
Energy required to heat a substance (mass m) to increase the temperature, or energy required to be taken away from a substance to decrease its temperature is:
ΔH = C ΔT = m s ΔT
Hence, for changing temperature of 1 gm substance by 1°Kelvin, or Centigrade, ΔH = s. If specific heat capacity is high, it takes more heat. So it is like electric resistivity to flow of electric current. For insulators, s is very high. So they do not allow flow of heat easily. They absorb a lot of heat before they allow heat to flow across them.