French Indefinite Demonstrative Pronouns

There are two kinds of demonstrative pronouns: variable demonstrative pronouns (celui, celle, ceux, celles) which agree in gender and number with their antecedent, and invariable (or indefinite) demonstrative pronouns (ce, ceci, cela, ça), which do not have an antecedent and their form does not vary.

Indefinite Demonstrative Pronouns

Invariable demonstrative pronouns, also called indefinite or neuter demonstrative pronouns, do not have a specific antecedent and thus do not have different forms for gender and number. Indefinite demonstrative pronouns can refer to something abstract, like an idea or a situation, or to something indicated but unnamed. On the other hand, a variable demonstrative pronoun refers to a specific, previously mentioned noun in a sentence; this pronoun must agree in gender and number with the noun it refers back to. 

There Are Four Indefinite Demonstrative Pronouns

1. Ce is the impersonal, simple indefinite demonstrative pronoun. It can mean "this" or "it," and is used mainly with the verb être, either in the basic expression c'est or in various impersonal expressions, which are expressions without a definite subject that begin with C​'est or Il​ est.

   C'est une bonne idée!
That's a good idea!

   C'est difficile à faire.
It's hard to do.

   C'est triste de perdre un ami. 
It's sad to lose a friend.

   Étudier, c'est important.
Studying is important.

Ce may also be followed by devoir or pouvoir + être.
Ce doit être un bon restaurant.
This must be a good restaurant.

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Learn About French Demonstrative Pronouns (Pronoms démonstratifs)

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   Ce peut être difficile.
This might be difficult.

A less common and more formal usage (especially in written French) of ce can be used without a verb:

   J'ai travaillé en Espagne, et ce en tant que bénévole.
I worked in Spain (and this) as a volunteer.
Elle l'a tué, et pour ce elle est condamnée.
She killed him, and therefore/for this she is condemned.

Note that ce is also a demonstrative adjective.
2. & 3. Ceci and cela are used as the subject of all other verbs:

   Ceci va être facile.
This is going to be easy.

   Cela me fait plaisir.
That makes me happy.

Ceci and cela are used with pouvoir or devoir when those verbs are not followed by être.

   Ceci peut nous aider.
This could help us.

   Cela doit aller dans la cuisine.
That has to go in the kitchen.

Ceci and cela can also be direct and indirect objects:

   Donnez-lui cela de ma part.
Give him this from me.

   Qui a fait cela?
Who did this?

Notes

Ceci is the contraction of ce + ici (this + here), while cela is the contraction of ce + là (this + there).

Ceci is rare in spoken French. Just as là commonly replaces ici in spoken French (Je suis là > I'm here), French speakers tend to use cela to mean either "this" or "that." Ceci only really comes into play when one wants to distinguish between this and that:

   Je ne veux pas ceci, je veux cela.
I don't want this, I want that.

4. Ça is the informal replacement for both cela and ceci.

   Donne-lui ça de ma part.
Give him this from me.
Qui a fait ça?
Who did this?

   Ça me fait plaisir.
That makes me happy.

   Qu'est-ce que c'est que ça?
What is that?

   Je ne veux pas ceci (or ça), je veux ça.
I don't want this, I want that.