In writing, double quotes are the punctuation marks that designate the exact words someone says or writes. They're particularly useful in dialogue, like when the murder mystery's detective says, "You're probably wondering why I've gathered you all here today."
In the U.S., a pair of double quotes is almost always used for dialogue, quoting sources, or emphasizing a specific word. If you want to quote Martin Luther King, Jr., you should put his words inside double quotes: "Injustice anywhere is a threat to justice everywhere." You can also use them to make a word stand out in a sarcastic way, like when your so-called "friend" forgets to invite you to their birthday party.