Easy.
To change the slogan or board description, log onto your board as Administrator.
Then (in the English menu) go to the 'Options' link on the 'Admin menu' on the left hand side of the page.
That header line can be changed right there at the top of the form under 'Board Description'.
When done, click 'Save Changes'.
That's the slogan changed.
To modify or add a logo, you have a variety of options.
You can do it by modifying the CSS alone for the specific style sheet you are using already. If you want a logo to show up in the title/header box for example, just modify the CSS that applies to the 'pun_title' CSS element to include a background image within your existing favorite style sheet.
Or you can include a logo above the punBB, or supply a separate header to run above punBB for example, by including the header HTML etc elements you want by editing the <your punbb>/include/main.tpl text file.
Etc.
More info: http://punbb.org/docs/faq.html