The term for a meaningful word part such as a prefix, suffix, or root is a morpheme.
Morphemes are the smallest units that carry meaning or grammatical function. A word may contain one free morpheme, such as “book,” or several morphemes, as in “books,” where “book” carries the main meaning and “-s” marks plurality. Prefixes and suffixes are usually bound morphemes because they cannot stand alone as words.
A root is the central morpheme in a word, while an affix is attached to it. This makes “morpheme” broader than “root”: a root is one type of morpheme, not a synonym for the whole category. The term belongs to morphology, the branch of linguistics that studies word structure.
Morphemes are easy to confuse with phonemes and allophones. A phoneme is a contrastive sound unit, while an allophone is a pronunciation variant; neither necessarily carries meaning. A digraph, meanwhile, is simply two letters representing one sound, as “sh” often does in English.