Matthew 5 has Jesus going up the mountain and chapter 8 has him coming down. These are followed by parallel passages which can be used to illuminate the meaning. The first thing Jesus says is, "Blessed are the poor in spirit." And the first thing Jesus does is heal a leper.
The next parallel is blessed are the meek, and the Centurion asks Jesus to heal his servant.
Just as the leper is an example of one poor in spirit, the Centurion is an example of one who is meek.
Structurally there are three blocks constructed with such parallelisms.
The word praüs is related to 'friend', denoting gentleness and pleasant, the opposite being rough, hard, violent. As an adverb it is used for a quiet and friendly composure which does not become embittered or angry at what is unpleasant. It is not a passive submission, but an active attitude and deliberate acceptance. As such, in the context of Jesus' words, it is one who actively turns the other cheek in a display of confidence in God. redacted from TDNT 6:645.
The Centurion knew the nature of authority, and it gave him the composure to speak with Christ in such a manner, recognizing that Jesus was the authority and being actively confident of a positive response.