"This apple is bad."
Translation:Dieser Apfel ist schlecht.
This is considered a demonstrative pronoun. When using "diese" in front of a noun, it takes on the ending that is associated with case (masculine, feminine, neuter). If the noun in front is masculine, it ends in ('-er or dieser), if it is feminine or plural, it ends in (-e or diese), if it is neuter, it ends in (-es or diese). Since "Apfel" is masculine (der Apfel), it will be dieser, not diese.
If you use 'Das' directly in front of a noun, it will take the role of the definite article (der/die/das) whereas if you place it in front of the verb it can be an demonstrative pronoun (like this/that in English). In the case that you are using an article, it must follow the gender of the noun, hence you could say either of these:
1 Der Apfel ist verdorben. (Apfel os masculine, hence 'der' for the subject, which takes the nominative case) 2 Das ist ein verdorbener Apfel. (Here 'das' is a demonstrative pronoun.)