The symbol you used in your example is indeed a hyphen, but you are using it to function as an em dash. So technically, you're using the wrong symbol.
The hyphen ( - ) should only appear in compound words and phrases (as in, eight-year-old, ex-wife, stick-in-the-mud, a part-time job, etc.).
The em dash ( — ) is best explained by the Chicago Manual of Style: Em Dashes are used to set off an amplifying or explanatory element and in that sense can function as an alternative to parentheses (second and third examples), commas (fourth and fifth examples), or a colon (first example)—especially when an abrupt break in thought is called for.
- It was a revival of the most potent image in modern democracy—the revolutionary idea.
- The influence of three impressionists—Monet, Sisley, and Degas—is obvious in her work.
- The chancellor—he had been awake half the night—came down in an angry mood.
- She outlined the strategy—a strategy that would, she hoped, secure the peace.
- My friends—that is, my former friends—ganged up on me.