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