So I was reading a book one day and I saw this. He gave her the 'Shut up look' is that correct? And, if so why? btw it was not in bold in the book.
They are not apostrophes. And what is between them is not a quotation. The marks are quotation marks. Single quotation marks in this case, also called inverted commas in the UK.
Style rules and preferences for choosing between single quotation marks (') and double quotation marks (") are apparently inverted between the U.S. and U.K. (Diffen).
Wikipedia identifies several cases where quotation marks may be used. But in this case, the usage may be better described in their article on "scare quotes". This article describes a more liberal set of rules for using quotation marks. The applicable paragraph states:
Alternatively, material in scare quotes may represent the writer's concise (but possibly misleading) paraphrasing, characterization, or intentional misrepresentation of statements, concepts, or terms used by a third party. This may be an expression of sarcasm or incredulity, or it may also represent a rhetorical attempt to frame a discussion in the writer's desired (non-standard) terms (e.g. a circumlocution, an apophasis, or an innuendo).
Immediately after that paragraph, in case you are confused by the term "scare quotes", it says
The term scare quotes may be confusing because the word scare implies provocation, yet the term covers emotionally neutral usage as well. In many cases an author uses scare quotes not to convey alarm, but to signal a semantic quibble.
You'll also note that in my quotations above, quotation marks are referred to as "quotes". I'm sorry to say that quotations are also referred to as "quotes", which can no doubt be confusing.