what is the deal now struck between the host, Bertilak and Gawain? How does this deal began to back fire on Gawai

The Green Knight is actually Bertilak de Hautdesert, servant to the sorceress Morgan le Fay. Gawain gallantly offers himself to battle for King Arthur. This was part of the Knight code of chivalry. The court agrees to let Gawain play, and after restating the terms of the agreement to each other, the stranger gives the battle-axe to Gawain, who cleaves off the stranger's head in one blow. But miraculously enough, the stranger does not die, and the body of the Green Knight picks up the severed head, which even speaks to Gawain. The stranger charges Gawain to meet him at the Green Chapel next New Year's morning, so that he may receive his exchange blow. Gawain eventually has to visit the Green Knight to offer up his neck.