καυχώμεθα kauchōmetha. The meaning is, that we rejoice not only in hope; not only in the direct results of justification, in the immediate effect which religion itself produces; but we carry our joy and triumph even into the midst of trials.  In accordance with this, our Saviour directed his followers to rejoice in persecutions, Matthew 5:11-12.  Compare James :2, James 1:12. (Dr. Albert Barnes)

 

But we glory in tribulations also - All the sufferings we endure for the testimony of our Lord are so sanctified to us by his grace, that they become powerful instruments of increasing our happiness.
Tribulation worketh patience - Ὑπομονην, Endurance under trials, without sustaining loss or deterioration. It is a metaphor taken from refining metals. We do not speak thus from any sudden raptures, or extraordinary sensations we may have of spiritual joy: for we find that the tribulations through which we pass are the means of exercising and increasing our patience, our meek forbearance of injuries received, or persecutions experienced, on account of the Gospel. (Dr. Adam Clarke)

 

Tribulation itself gives us different and various occasions to rejoice, and more than this it does not make us miserable. Afflictions make us use to being patient, and patience assures us of the goodness of God, and this experience confirms and fosters our hope, which never deceives us. (Geneva Bible Translation Notes)