Relative pronouns begin adjective clauses:

the man that was here

the man that I saw

Qui /ki/ is the subject of the clause it introduces:

J’aime les chiens qui sont calmes.^{I like dogs that are quiet.}

Que /kə/ is the direct object of the clause it introduces:

C'est un homme que je connais très bien.^{He's a man whom I know very well.}

Remember that in perfect tenses, the past participle agrees with the direct object in gender and plurality if the direct object comes before the verb:

Elles sont les femmes que j'ai vues.^{They are the women that I have seen.}

If que is followed by a vowel, it is shortened to qu' :

Il est l'homme qu'elle a vu.^{He is the man that she has seen.}