Almost every modern website has a header section which shows up on the top in almost every page within the website.
The new "header" element is meant for that.
Actually, I was just joking. "header" element is meant more than just that. We are encouraged to use use "header" element for so-called masthead (master head) of a website.
By the way, I didn't mean "New York Times" actually uses "header" element. I mean "New York Times" can use "header" element for that.
However, we mustn't think that "header" is only for masthead of a website. "header" can be use as a heading of an blog entry or news article as every article has its title and published date and time.
Not only that, we mentioned in previous "section", each section should have probably have its heading.
The "header" element usually contain header elements (h1 to h2 or hgroup), however this is not a requirement, even it is commonly practised.
Similarly to what we have learnt in "section", "header" element has its own outline, you can happily define your own h1,h2..h6 without worried what has been defined in its ancestor.