What is it called when you give credit in your writing to someone else's quote?

Answer: citation

There are two basic ways to give credit to another person in your writing.

(a) The use of a signal phrase.

For example, you might write this:

According to John Doe (2005), Author of "Old Classic Novels", it is necessary to understand ...

(b) In-Text Citation.

For example, you might write:

It is necessary to understand ... (John Doe, 2005, p. 65-70)

In this case, the reference is provided at the end of the article or as a footnote.