‘Ata bin Sa’ib says: Muharib bin Dithar said to me: Have you heard anything from Sa‘id bin Jubayr about al-Kawthar from Sayyiduna Ibn ‘Abbas (may Allah be pleased with them both)? He said: Yes, he has said that al-Kawthar means abundant good. Muharib said: Subhan Allah, the statement of Ibn ‘Abbas (may Allah be pleased with them both) is indeed reliable. I heard Sayyiduna Ibn ‘Umar (may Allah be pleased with them both) saying: When {إِنَّاأَعْطَیْنَاکَالْکَوْثَرَ} was revealed, the Noble Prophet (peace and blessings be upon him) said: This is a river in Paradise, its banks are of gold, it flows in channels of pearls and rubies, its water is sweeter than honey, whiter than milk, colder than ice, and more fragrant than musk. Sayyiduna Ibn ‘Abbas (may Allah be pleased with them both) spoke the absolute truth. By Allah! This is indeed abundant good and blessing.
Hadith Referenceالفتح الربانی / تفسير من سورة الأعلى إلى سورة الناس / 8843
Benefits: … Sayyiduna Abdullah ibn Abbas radi Allahu anhuma said: “Al-Kawthar is the abundant good which Allah has given to him.” Abu Bishr said: I said to Sa‘id: “There are people who claim that it is a river in Paradise?” Sa‘id replied: “The river which is in Paradise is also from the good which Allah has given to him.” … By al-Kawthar is meant that abundant good which Allah the Exalted has granted to you (sallallahu alayhi wa sallam). Abu Bishr said: I said to Sa‘id: People think that al-Kawthar is the name of a river in Paradise. He replied: The river in Paradise is also from among the good which Allah the Exalted has granted to you (sallallahu alayhi wa sallam). (Sahih Bukhari: 6578)
Various meanings of al-Kawthar have been mentioned; from these marfu‘ (attributed to the Prophet) hadiths it is established that by it is meant a river which will be granted to you (sallallahu alayhi wa sallam) in Paradise. In some hadiths, its referent has been described as a reservoir (hawd), and the water in this reservoir will come from that river in Paradise. Hafiz Ibn Kathir has given preference to the meaning of “abundant good,” because in this are included all the blessings which you (sallallahu alayhi wa sallam) will receive in this world and the Hereafter.