Although the band have never given an explanation as to what it means to them personally, the entire paragraph, as it was presented on the website, read:
fght ff yr dmns. wrt sngs n yr slp. fight yr dmns your DEMONS. w lv y. w mss y. i lv y s mch tht t hrts m hd.
(Translation for anyone who cant be bothered to work it out - fight off your demons. write songs in your sleep. fight your demons, your demons. we love you. we miss you. i love you so much that it hurts my head)
It remains unclear, to me at least, why there is use of vowels in two of the words and none of the others, unless it is merely for added emphasis.
Also, the line "I love you so much that it hurts my head" occurs in the song Degausser, which is from the newest album 'The Devil and God Are Raging Inside Me'.
Brand New must still be using the phrase "fight off your demons/fght ff yr dmns' as it is splashed across the t-shirts sold to promote the new album (which makes sense - there seems to be a lot of Biblical reference incorporated into this album, and if Jesse Lacey has the Devil and God raging inside him, then it goes hand in hand that he'd be fighting off his demons).