"Primary, secondary, tertiary" refers to the degree of hydrocarbyl substitution on the ammonia molecule.
Explanation:
Ammonia is NH_3. A primary, 1""^@, amine is RNH_2, that is it has one hydrocarbyl substituent on nitrogen. A secondary, 2""^@, amine is R_2NH, and a tertiary, 3""^@, amine is R_3N. A quaternary ammonium salt is R_4N^+.