What is the meaning of the saying of Ibn Mas'ud, may Allah be pleased with him: "No prophet among the prophets was distressed except that he sought help through glorification (tasbih)"?

This narration from Ibn Mas'ud, may Allah be pleased with him, indicates that theb Prophets would seek help through tasbeeh (glorification of Allah) during hardships. This is a legitimate form of seeking intercession through good deeds. The meaning of "sought help through tasbeeh" is that they sought help by praising Allah and declaring Him free from all imperfections. Praise may stand in place of supplication or include it.

This is supported by Allah's words in the story of Yunus (Jonah), peace be upon him: (AND [MENTION] DHUN-NUN [YUNUS], WHEN HE WENT OFF IN ANGER, SUPPOSING THAT WE WOULD NOT RESTRICT HIM. BUT HE CALLED OUT IN THE DARKNESS, "THERE IS NO DEITY EXCEPT YOU; EXALTED ARE YOU. INDEED, I HAVE BEEN OF THE WRONGDOERS." SO WE RESPONDED TO HIM AND SAVED HIM FROM THE DISTRESS. AND THUS DO WE SAVE THE BELIEVERS.) [21:87-88] And His saying: (AND IF HE HAD NOT BEEN OF THOSE WHO GLORIFY [ALLAH], HE WOULD HAVE REMAINED IN ITS BELLY UNTIL THE DAY THEY ARE RESURRECTED.) [37:143-144].

It is possible that the Prophets would offer tasbeeh and praise to Allah before supplicating in distress, as indicated by the hadith of Fadalah ibn Ubaid, and the Prophet's, peace and blessings be upon him, saying regarding the supplication of Dhun-Nun: (Shall I not inform you of something, that if distress or an affliction from the afflictions of this world befalls one of you, and he supplicates with it, it will be relieved for him? It is the supplication of Dhun-Nun: "There is no deity except You; exalted are You. Indeed, I have been of the wrongdoers.")

So, tasbeeh is a powerful means by which Allah relieves distress from His believing servant, whether he is a Prophet or otherwise.