An inflected word form is composed of a lexical component and a component comprising the values of morphological categories for which it is specified. For the coding of these two components in morphological structure, there are two major possibilities:

• Both components are coded in one word form. This is a synthetic form of the respective inflection paradigm.
• The lexical component is coded by a (lexical) word and the grammatical component is coded by grammatical formatives which constitute at least one additional word. This is an analytic form of the respective inflection paradigm.

For instance, the English conjugation paradigm comprises the following forms:

This conception and terminology were introduced in Schlegel 1818. Since then, the terms have sometimes be reused. An analytic form is often called periphrastic.

Reference

Schlegel, August Wilhelm von 1818, Observations sur la langue et la littérature provençales. Paris: Librairie grecque-latine-allemande.