(and glorify the praises of their Lord, and they are not proud.) means, they are not too proud to follow them and submit to them, unlike the ignorant among the rebellious disbelievers. Allah says:
Before approaching verse 16: تَـتَجَافٰى جُنُوْبُهُمْ عَنِ الْمَضَاجِعِ يَدْعُوْنَ رَبَّهُمْ خَوْفًا وَّطَمَعًا (Their sides remain apart from their beds. They call their Lord with fear and hope - 16), it should be borne in mind that disbelievers, Mushriks and the deniers of the day of Qiyamah were warned in the verses previous to it. After that, starting from: اِنَّمَا يُؤْمِنُ بِاٰيٰتِنَا ! (Only those people believe in Our verses - 15) mentioned there are special attributes of sincere believers and the high ranks reserved for them. Pointed to in the cited verse is one such attribute of these believers: They leave the comfort of their beds, rise and get busy with the remembrance of Allah in submission and supplication - because, they are apprehensive of His displeasure and punishment while remaining hopeful of His mercy and reward. This very combination of fear and hope keeps them returning to Dhikr and Du'a' repeatedly, anxiously and animated at the same time.
For an individual to avail of guidance, his willingness to accept the Truth is the most important factor. Only those who, by temperament, are ready to accept the Truth whenever it presents itself before them—whether it be revealed through a person of lesser importance, whether such acceptance be a tacit admission of one’s own error, or whether such acceptance leads to upsetting the existing system of one’s life—are capable of availing of guidance. Only those who have such a capacity will find the Truth. Those who want to accept the Truth, but at the same time want their ‘greatness’ to remain intact, will never find it. A man who sacrifices his greatness for the sake of Truth actually finds the greatest thing, namely, the greatness of God. God enters his life in such a way that he sleeps thinking about Him and wakes up with memories of God. His hopes and fears are all linked with God. He surrenders all his possessions to God to the point of not keeping back anything for himself. Such people will forever relish the bounties of the eternal Gardens of Paradise.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.