A homologous series is a series of carbon compounds that have different number of carbon atoms but contain the same functional group.
For example: methane, ethane, propane, butane, etc. are all part of the alkane homologous series. The general formula of this series is CnH{2n+2}.
Methane: CH4
Ethane: CH3CH3
Propane: CH3CH2CH3
Butane: CH3CH2CH2CH3
It can be noticed that there is a difference of -CH2 unit between each successive compound.