الحمد لله / الحمد لله رب العالمين
al-Ḥamdu li-llāhi / al-Ḥamdu li-llāhi rabbi l-ʿālamīn
Praise and thanksgiving to Allah, Lord of the universe, said at the end of any activity.
What it means
The longer form is the second verse of the Fatiha, “Praise be to God, Lord of the worlds” (1:2). The Quran says that the last prayer of those in Paradise will be “Praise be to God, Lord of the worlds” (10:10), and the same words close the account of the judgment (39:75). Muslims therefore use them to end a task, a speech or a prayer. The phrase unites praise and gratitude and ascribes every success to God. It is among the most frequent words on Muslim lips.
What the sources say
A hadith in Sahih Muslim, reported by Abu Malik al-Ashʿarī, says that al-ḥamdu li-llāh fills the scale of deeds.
Term and Arabic as listed in Ismail al Faruqi, Toward Islamic English (International Institute of Islamic Thought, 1995), p. 56, listed as AL ḤAMDU LILLAHI or AL ḤAMDU LILLAHI RABB AL ‘ĀLAMĪN. The definition is restated here.