Specific heat capacity or SHC is defined (In chemistry at least) as: The amount of energy required to raise one gram of a substance by one kelvin. 

Due to the weights of different molecules lighter substances contain more particles for a given weight and because all the particles are heated evenly (due to the property that a closed systems will seek to obtain a thermal equilibrium) lighter substances will have a higher SHC because there are more particles per gram 


The SHC of Hydrogen, which has an atomic weight of 1.008 AMU's is ~14.3 

The SHC of Oxygen, which has an atomic weight of 16 AMU's is ~0.918 

As you can see because hydrogen is ~16 times smaller than Oxygen, the increased number of particles per gram means that a lot more energy is required to raise them all by one kelvin 

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Specific heat capacity of a substance is the amount of heat needed by 1 Kg of the given substance (water, etc..) by 1°C.
Different substances have different heating capacity because the amount of heat needed by them to heat up and increase the temperature by 1°C is different.
Specific heat capacity of water is 4200 J/Kg°C
But specific heat capacity of Kerosene Oil is 2100 J/Kg°C.
Here, water needs more amount of heat to increase the temperature by 1°C when compared with Kerosene Oil.
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