The Essence
Al-Qayyum is the Self-Sustaining Sustainer of all. He needs absolutely nothing to exist, yet every single atom in the universe relies entirely upon Him for its continued existence every fraction of a second.
In the Quran
اللَّهُ لَا إِلَهَ إِلَّا هُوَ الْحَيُّ الْقَيُّومُ
"Allah - there is no deity except Him, the Ever-Living, the Sustainer of [all] existence (Al-Qayyum). (Surah Al-Baqarah 2:255)"
In Your Duas
يَا حَيُّ يَا قَيُّومُ بِرَحْمَتِكَ أَسْتَغِيثُ، أَصْلِحْ لِي شَأْنِي كُلَّهُ
"O Ever-Living, O Sustainer (Qayyum), by Your mercy I seek assistance, rectify for me all of my affairs."
— Mustadrak al-Hakim 1/545