Parliament, known officially as the Valendia National Council, is the governing body of the New Valendian Kingdom in Vagrant Story. It is based in the capital city of Valnain where it shares power with the constitutional monarch. Under Parliament's direct control is the Valendia Knights of the Peace. It is largely controlled behind the scenes by Duke Bardorba.
During the VKP meeting with Ashley Riot, several members of Parliament could be seen in the shadows. Apparently there is dissatisfaction amongst the Parliament members on Duke Bardorba's control over the Parliament's decision-making. As the story progresses, Ashley will learn that there is more to this than what the Parliament and the VKP lets out.
A parliament is a legislature. More generally, "parliament" may simply refer to a democratic government's legislature.