Everyone knows that one little line that looks like this ' is an apostrophe, and is used either to show missing letters or possession. Everyone also knows that two little lines that look like this " is a quotation mark, and is used when you are making a direct quote. However, what if your book character is speaking, and quoting something someone else already said?
That's when you need to know how to use single quote marks as well as double quote marks. Here's how they work.
If I am quoting something Jim said, I would write: Jim said, "Let's go to the store."
If I am quoting something Jim said, and he is quoting Steven, I would write: Jim said, "I wish more people would listen to my friend Steven when he says, 'People should live by the golden rule.' Then the world would be a much nicer place."
Note that what Steven said has single quote marks, while everything that Jim said, both before and after Steven's sentence, is enclosed in double quotation marks.
Although this happens fairly often in real life, as a general rule, don't do this often in fiction because it can be confusing to your readers.