Demonstrative adjectives (this, that, these, those) are words used in place of articles to indicate a specific noun. In French, they must agree in gender and number with the noun they modify:

Ce is the masculine singular demonstrative adjective:

Ce prof parle trop. – This (That) teacher talks too much.
J’aime ce livre. – I like this (that) book.

Ce becomes cet in front of a masculine noun that begins with a vowel or mute h (learn more):

Cet homme est sympa. – This (That) man is nice.
Je connais cet endroit. – I know this (that) place.

Cette is feminine singular:

Cette idée est intéressante. – This (That) idea is interesting.
Je veux parler à cette fille. – I want to talk to this (that) girl.

Ces is plural:

Ces livres sont stupides. – These (Those) books are stupid.
Je cherche ces femmes. – I’m looking for these (those) women.

Notes:

Ces is the only plural demonstrative adjective: « cettes » does not exist.

The singular demonstrative adjectives cecet, and cette can all mean « this » or « that. » Your listener can usually tell by the context which you mean, but if you want to stress one or the other, you can use the suffixes -ci (here) and -là (there):

Ce prof-ci parle trop. – This teacher talks too much.
Ce prof-là est sympa. – That teacher is nice.
Cet étudiant-ci comprend. – This student understands.
Cette fille-là est perdue. – That girl is lost.

Likewise, ces can mean « these » or « those, » and again you can use the suffixes to be more explicit:

Je veux regarder ces livres-là. – I want to look at those books.
Je préfère ces pommes-ci. – I prefer these apples.
Ces fleurs-ci sont plus jolies que ces fleurs-là. – These flowers are prettier than those flowers.

The demonstrative adjective ce does not contract – in front of a vowel it changes to cet. So c’in the expression c’est is not a demonstrative adjective: it is an indefinite demonstrative pronoun.

Test on French demonstrative adjectives

Related lessons: Demonstrative pronouns | Ces vs Ses

English Masculine Masc before vowel Feminine
this, that    ce    cet    cette
these, those    ces    ces    ces