Composed by the incredible Ramin Djawadi, it's the theme for House Lannister: it's a majestic theme that is going to be developped thoughout the seasons in many ways. In fact, I've remade the cue entitled "A Lannister Always Pays His Debts": this is a more heroic version of the motif, associated with Jaime Lannister. The melody in Dm, played at first by a solo cello, is very similar to the one of "Lost but Won". As Ramin Djawadi has said in some interviews, to make the soundtrack of GoT he used mainly instruments that could be associated with the Medieval era: it's no surpirse then that the orchestration of the piece is built over the strings and the percussion. 

"The Rains of Castamere" is a song about the distruction of the rebel house Reyne of Castamere, written to commemorate Tywin Lannister's overwhelming victory. It's usually sung to remember the fate of whoever dares to stand against the Lannisters