Heat capacity
Heat capacity is a measure of how much materials can store up heat as they change temperature.
Materials with high heat capacities require a lot of heat to be stored up before a small change. Materials with low heat capacities require very little heat to be stored up before a large change.
Specific heat is based on temperature (for molecules) and will often be denoted as Cp(T) in thermochemical calculations. The dependence on temperature comes from the fact that at low energies some modes of molecular movement may not be available to the molecule until the energy rises, an example being: H2 molecules acting monatomic until energy rises to allow to light hydrogen atoms to hold energy through rotational modes. Because of this, monatomic particles such as He have a constant specific heat (ignoring intermolecular/quantum effects) due to the only energy storage means being translation in X, Y, and Z.
The heat capacity of one gram (or some other unit of mass) of a material is called the specific heat capacity of the material, so that the heat capacity of something is its mass times its specific heat capacity.
Specific heat capacities are often listed in tables, like this one: [1]