Catholics, Orthodox, and other denominations hold that the definitions produced by accepted ecumenical councils are protected from error by the Holy Spirit.
What is the manner of this inspiration? Does that mean these definitions should be treated with the same authority and reverence as accorded for Scripture?
Ecumenical councils derive their authority from the pope who ratifies the councils' documents, so your question amounts to asking about papal infallibility or how a pope defines a dogma.
cf. also: "Creed, Encyclical, Decretal, Canon, Bull, etc - What's the difference?", "The Church's Theological Notes or Qualifications"
Also, St. Robert Bellarmine—Book II, ch. XII of On Councils: Their Nature and Authority (from his De Controversiis)—compares the authority of Holy Scriptures to that of councils:
Catholics do not subject the Sacred Scripture to Councils, but places it before them; nor is there any controversy on this point. But if some Catholics sometimes say scripture depends upon the Church, or a Council, they do not understand this in regard to its authority, or according to what it is, but in regard to the explanation and in regard to us.
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