A sentence is said to be negative (une phrase négative) when it denies/negates something.

A negative sentence is one such as "Il n'aime pas le beurre" [He doesn't like butter] - it is  neither affirmative (Il aime le beurre) nor interrogative (Aime-t-il le chocolat). 

There are actually two negative words strictly speaking: non and ne.

The other negative expressions such as pas [not], plus [no longer, no more], jamais [never], rien [nothing, anything], nullement [by no means, not at all], aucun [not a..., no], du tout [at all], nulle part [nowhere]  and so on are accessories that more often than not serve as complements of the former two.

Ne can be used as a stand-alone word (without other negative words like pas, or rien). We then talk of "weak" negation.

In front of some specific verbs + infinitive, ne doesn't always need another complement --> Je ne peux le faire (I can't do it), je ne cesse de vous le dire (I keep telling you this again and again), je n'ose le dire (I don't dare saying it)

Ne is used alone as in the ne explétif case. (See the section on expletive ne)

In everyday spoken French, people will often omit ne as in "Je sais pas" (I don't know). 

Ne...pas is halfway between the weak negation (ne only) and the strong negation ne...point.

 

In certain expressions, too only ne gets used, (called ne expletif) (e.g. Evitez qu'elle ne vous parle - Avoid letting her talk to you.) but in that context, the presence has no negative value or effect. In fact the ne explétif is optional.

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Here are a few French sentences in the negative form.

1. Je ne bois jamais de café. I never drink coffee. 
2. Cette réponse n'est pas juste. / This answer isn't correct.
3. Elle n'est plus la directrice de ce collège. She is no longer the director of his university.
4. Nous ne voulons rien manger.  We don't want anything to eat.

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