The link text is usually from the page's <title> element. The text in black following is sometimes taken from the page's <meta name=description>, and sometimes

The link text is usually from the page's <title> element. The text in black following is sometimes taken from the page's <meta name=description>, and sometimes from text on the page Google feels is relevant. I think that is what you mean by "header" and "subheader"; if not, please clarify.