Quick extension to Francesco's answer...
While a human being can easily distinguish what is the header and what is the footer on a webpage, a computer program will have hard time at making this kind of inferences.
Better to say "while a sighted human can visually distinguish the header and footer..." because these elements provide useful information to people using assistive technology like screen readers and braille printers.
That is, these elements are for accessibility - SEO is a bonus but not the primary reason semantic markup was defined in the specs.
If you are working on a system that only allows DIVs you can add equivalent functionality using ARIA, but the W3C's recommendation is to use native HTML where possible.