A banner is also known as a  banner ad. A banner is an advertisement placed on top, bottom or on the sides of an website. On a banner there could be a text or animated pictures or be flashy.

A header is a rectangular box that goes across the top of an website. The purpose of the header is it advertises and promotes your website. Also it it is important because that's how people recognize what your website is and what it is about.

The differences between the header and a banner is A banner is mostly used on other websites to advertise your website and a header is used on your website to tell people what the website is about.