“Personal” or “conjugated” as referring to a verb means a verb that is marked for person (1st, 2nd, or 3rd) and number (singular or plural) and can serve as the principal verb of a clause or sentence. It is called personal, because it is marked for person:
- I am a human bean. You are a wandering knight. She is a damsel in distress.
- He has many enemies. I have many friends.
- I run the kitchen. He runs the store.
In French, there is a different form (almost) for every person-&-number combination:
- Il marche rapidement. Nous marchons péniblement. Tu marches délicatement, etc.
Such a verb form is also called conjugated, because it is differently formed for person and number as well as other things (tense, mood…). (In other words, “conjugated” and “personal” are pretty much identical.)
A personal verb form is in addition independent when it stands as the principal verb of a clause or sentence; together with the subject, it forms the core of the clause.
What are not personal-conjugated-independent verb forms? Any form not marked for both person and number. These forms cannot serve by themselves as the principal verb of a clause. They are:
- parler, finir, rendre, avoir, être, etc. (to speak, to finish, to give back, to have, to be, etc.)
- Present: parlant(e), finissant, rendant, ayant, étant, etc. (speaking, finishing, giving back, having, being, etc.)
- Past: parlé(e), fini, rendu, eu, étant (spoken, finished, given back, [having been] had, been, etc.)