It has the sound of either an unvoiced dental fricative, like th (such as in the English word "thick") or the voiced form (such as in English "the"), though in Icelandic the usage is restricted to the former.
It was used in writing Middle English before the invention of the printing press: Caxton, the first printer in England, brought with him type made in Continental Europe, which lacked thorn, yogh, and edh. He substituted "y" in place of thorn, and in fact "y" is still often substituted for it on gravestones and quaint store signs: "ye olde candies shoppe" should be read as "THe olde....", although it is jocularly pronounced "yee". This was not an arbitrary choice of Caxton's; in some manuscripts of the earlier 1400s (e.g. The Boke of Margery Kempe) the letters "y" and thorn were identical.