Dont is a relative pronoun that replaces de + noun to join two clauses together into one sentence.

Je rêvais d'une voiture. Cette voiture était rouge et très performante.
(I was dreaming of a car.) (This car was red and very powerful.)

La voiture dont je rêvais était rouge et très performante.
(The car (that) I was dreaming about was red and very powerful.)

Dont can refer to both people and things.

Dont is very similar to que, except that it is used to replace nouns that are preceded by de.

Je regardais une voiture. Voilà la voiture que je regardais.
Je rêvais d'une voiture. Voilà la voiture dont je rêvais.

Dont will often be used, therefore, with verbs that take de + noun, such as avoir besoin de (to need), penser de (to think of (in terms of opinion)), parler de (to speak of/about), se souvenir de (to remember.)

Je crois que j'ai vu le film dont tu parles.
(I think I have seen the film (that) you are speaking about.)

  • dont replaces a repetition of 'd'un film':
                                Tu parles d'un film.
                        Je crois que j'ai vu le film.

Dont is used to replace all nouns preceded by de, whether they are masculine or feminine, singular or plural

Since de is often used to indicate possession, dont will also often indicate possession.

Cédric Klapisch, voilà un réalisateur dont les films sont toujours très humoristiques. (Cédric Klapisch, there's a director whose films are always very funny.)
            (Les films de Cédric Klapisch sont toujours très humoristiques.)

Cédric Klapisch, voilà un réalisateur dont j'admire les films.
(Cédric Klapisch, there's a director whose films I really admire.)
             (J'admire les films de ce réalisateur.)

(Notice the difference in word order between French and English in this second example: in French 'les films' does not have to follow the dont directly, but remains in its typical place in the sentence: since 'les films' is the object, it comes after the verb.)

Also notice the different use of articles:

in English, 'whose' incorporates the article:
         'the films of Cédric Klapisch' becomes 'Cédric Klapisch, whose films...'

in French, dont doesn't incorporate the article:
         'les films de Cédric Klapisch' becomes 'Cédric Klapisch, dont les films...'