The term “demonstrative pronoun” describes a word that is used to refer back to another noun or pronoun of a previous sentence or conversation, or to put emphasis on a specific noun or pronoun. 
In English, we typically think of “this, that, these, those” as the demonstrative pronouns. 
In German, quite a few more articles can be used as demonstrative pronouns. It is important to pay attention to the case of the noun or pronoun that we refer back to. 

1. The definite article as a demonstrative pronoun

Whenever we deal with nouns and their articles in German, we also deal with genders and cases. When we use a definite article as a demonstrative pronoun, then we have to pay attention to the gender of the noun, and what case the noun is in. 
The chart for definite articles as demonstrative pronouns is identical to that of relative pronouns. The difference is that a demonstrative pronoun does not introduce a relative clause, but can stand alone. 

Examples:
Kennst du den Mann? Nein, den kenne ich nicht. 
Do you know the man? No, I don’t know him. 

Hast du die Blumen mitgebracht? Nein, die habe ich vergessen. 
Have you brought the flowers? No, I have forgotten those. 

Notice how in both German sentences, the article is not accompanying a noun. “den” and “die” are used as demonstrative pronouns, referring back to a noun (the man and the flowers) in a previous sentence or conversation. 

2. Dies-

We use “dies” + case endings when we want to refer to a specific noun. “Dies-” can be used as a demonstrative “article”, together with a noun (dieser Mann, diese Frau, etc), but when used by itself, referring back to a noun that was previously mentioned. 

The case endings for “dies-” as a demonstrative pronoun are the same as those for demonstrative articles:

Examples:
Kennst du diesen Mann? (demonstrative article, masculine noun, accusative). 
Do you know this (specific) man? 
Nein, diesen kenne ich nicht. (demonstrative pronoun, masculine noun, accusative). 
No, this (specific) one I don’t know. 

3. “jen-“

“Jen-” could be compared to “that” or “those” in English. The case endings are the same for “jen-” as a demonstrative article and “jen-”  as a demonstrative pronoun, and they are identical to those of “dies-“. 

Examples:
Kennst du jenen Mann? (demonstrative article, masculine noun, accusative)
Do you know that man? 
Nein, jenen kenne ich nicht. Aber diesen kenne ich. (demonstr. pronoun, masc. acc.)
No, that one I don’t know, but this one I know. 

4. “-selb-“

“-selb-” is a bit more complicated as the other examples, as it requires a case- and gender-specific definite article as a prefix, and a case ending as a suffix. It is used to refer back to “the same” noun. If used with a noun, it would be considered a demonstrative article, but it is only a demonstrative pronoun if used by itself. 

Examples:
Ist das derselbe Mann? Ja, das ist derselbe. 
Is this the same man? Yes, it is the same. 

Schaust du denselben Film an? Ja, ich schau denselben an. 
Are you watching the same movie? Yes, I’m watching the same one.