There is a philosophical difference between using a word and mentioning it.
For example, the statement “That bike is blue" uses the word “blue” while the statement “The sign said, 'Blue bikes for sale'” only mentions the word “blue”.
Why is this distinction important?
In the context of "objectionable language", the use-mention distinction holds that mentioning a slur or taboo word when discussing it or quoting it accurately is not morally equivalent to using it.
In the context of political or cultural discourse, the use-mention distinction helps you spot it when people try name of a thing with the thing itself. This is typically done in order to control how that thing is viewed by others. For example, labeling speech you don't like as "hate speech" makes it difficult for people to defend it without sounding, well, hateful.