Obviously, the second thing that you are going to do after you have made changes to your Moodle header file is carry on and change the footer.html file. The following tasks will be slightly easier than changing the header logo and title text within your Moodle site, as there is much less code and, subsequently, much less to change.
The first thing that you will notice about the footer in Moodle is that it has the Moodle logo on the front page of your Moodle site and a Home button on all other pages. In addition to this, there is the login info text that shows who is logged in and a link to log out.
More often than not, Moodle themers will want to remove the Moodle logo so that they can give their Moodle site its own branding. So get stuck in with the next exercise, but don't forget that this logo credits the Moodle community.