We begin the section known as the Psalms of Ascent, or Degrees. (120-134) Tradition holds that there were sung or repeated by those making pilgrimage to Jerusalem during the feasts. There is not total agreement that they have any such intent, nor is there agreement on if they were to be sung at those times.
All that to say, we can't be dogmatic on why they are called by that title, but we can say that the faithful Jewish man or woman, then or now, should hold them with that level of regard. The church should also have the same reverence for our assembling together when we meet as His body.
They are magnificent and great to focus the heart and mind that our God meets us when we come to Him.