The carbon atom adjacent to the functional group is known as alpha carbon atom .The hydrogens attached to such a carbon atom are called as alpha hydrogen atoms. For example in CH3CH2COOH the hydrogen atoms of CH2 ( the carbon adjacent to functional group COOH ) are alpha hydrogen atoms. If one of the hydrogen atom of this acid is replaced say be amino group the resulting compound CH3CH(NH2)COOH is known as alpha amino acid. Like this it is used in nomenclature as well as while discussing the reactivity of compounds the alpha hydrogen plays an important role ( whenever it is involved).