late 14c., "something brought forward, a proposition, assertion, or argument" (a sense now obsolete), from Old French motif "will, drive, motivation," noun use of adjective, literally "moving," from Medieval Latin motivus "moving, impelling," from Latin motus "a moving, motion," past participle of movere "to move" (from PIE root *meue- "to push away").
Meaning "that which inwardly moves a person to behave a certain way, mental state or force which induces an action of volition" is from early 15c. Hence "design or object one has in any action."
verbal suffix for Latin verbs in -are, identical with -ate (1). Old English commonly made verbs from adjectives by adding a verbal ending to the word (such as gnornian "be sad, mourn," gnorn "sad, depressed"), but as the inflections wore off English words in late Old and early Middle English, there came to be no difference between the adjective and the verb in dry, empty, warm, etc. Thus accustomed to the identity of adjectival and verbal forms of a word, the English, when they began to expand their Latin-based vocabulary after c. 1500, simply made verbs from Latin past-participial adjectives without changing their form (such as aggravate, substantiate) and it became the custom that Latin verbs were Englished from their past participle stems.