Snake had succeeded in his mission, partly with the help of an agent called EVA, who tells Snake not only the truth about her own mission (she wasn't working for the KGB, but for the Chinese), but also the Boss, who was actually working for the US government all the time. He's learnt, effectively, that the government screwed her over and sacrificed her so that they could get a hold of a vast resource of funds known as the Philosopher's Legacy from Volgin.
By the way, that name, Big Boss? If it sounds weird to you, Big Boss is the villain of the first two
Metal Gear games, and
Metal Gear Solid 3 was actually the first game to look at Big Boss' past, and why he turned against the US.