Materials with high heat capacities require a lot of heat to be stored up before a small change in temperature can be measured. Materials with low heat capacities require very little heat to be stored up before a large change in temperature can be measured.
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: 
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Constant volume specific heat capacity of diatomic gases (real gases) between about 200 K and 2000 K. This temperature range is not large enough to include both quantum transitions in all gases. Instead, at 200 K, all but hydrogen are fully rotationally excited, so all have at least 5/2 R heat capacity. (Hydrogen is already below 5/2, but it will require cryogenic conditions for even H2 to fall to 3/2 R). Further, only the heavier gases fully reach 7/2 R at the highest temperature, due to the relatively small vibrational energy spacing of these molecules. HCl and H2 begin to make the transition above 500 K, but have not achieved it by 1000 K, since their vibrational energy level spacing is too wide to fully participate in heat capacity, even at this temperature.
The dimensionless heat capacity divided by three, as a function of temperature as predicted by the Debye model and by Einstein’s earlier model. The horizontal axis is the temperature divided by the Debye temperature. Note that, as expected, the dimensionless heat capacity is zero at absolute zero, and rises to a value of three as the temperature becomes much larger than the Debye temperature. The red line corresponds to the classical limit of the Dulong–Petit law
Heat capacity Facts for Kids. Kiddle Encyclopedia.