The one who has perfect power, existing in and of Himself and not dependant upon anyone else. The sustainer of the inhabitants of the heavens and the earth, the one who regulates their affairs and provisions. The name al-Hayy includes all of the Attributes of His Self and the name al-Qayyum includes all the Attributes of His Actions.
“Allah! There is no deity worthy of worship but Him, al-Hayy, al-Qayyum.”
[Ali 'Imran (3): 2]
“All faces shall be humbled before [Allah], al-Hayy, al-Qayyum. And the one who carried the burden of wrong-doing shall be in complete loss!”
[Ta Ha (20): 111]
From “Explanation to the Beautiful and Perfect Names of Allah” — Shaykh as-Sa’di (d.1376H)