A header is a separate bit of text at the top of a printed page. A header might be the title of the novel you're reading, which is repeated on each page of the book.
One kind of header — also called a "page header" — is a chapter title, which is often printed at the top of every page. It's called a header because it's printed at the top, or head, of the page. When you format a long paper for school, you may include page numbers as headers. In any case, a header is set apart from the main text of a document and is sometimes printed in a larger or bolder font.