A functional morpheme is a morpheme

Morpheme

In linguistics, a morpheme is the smallest semantically meaningful unit in a language. The field of study dedicated to morphemes is called morphology. A morpheme is not identical to a word, and the principal difference between the two is that a morpheme may or may not stand alone, whereas a word,...

 which simply modifies the meaning of the word, rather than supplying the root meaning of the word. That is to say that it functions, but does not mean in and of itself. Examples include inflectional morphemes, like -ing (present tense) and -ed (past tense) and simple affixes like a(n)- (from the Greek, a negation prefix) and -able.