Progress for Bury means that civilization has moved, is moving, and will move in a desirable direction. But desirable is a questionable term and there may there be impassable barriers ahead. Perhaps there are limits to human understanding or ability to investigate.
Progress is a hypothesis which may or may not be true and cannot be proved either true or false. Belief in it is an act of faith. It is based on an inter-pretation of history that regards human beings as slowly advancing in a definite and desirable direction, and infers that this progress will continue indefinitely. It is of comparatively recent origin. The intellectual climates of classical antiquity and the ages after did support such a belief until the idea began to be expressed by some thinkers in the sixteenth century.