Quraysh (قريش) is the name of a tribe most notable for the fact that the prophet of Islam, Muhammad (صلى الله عليه وسلم) was born in one of its clans, the Banu Hashim.
Ali ibn Abi Talib (رضي الله عنه) was asked about Quraysh, when he replied:
"As for Banu Makhzum they are the blossoms of Quraysh. It is delightful to talk to their men and marry their women. As for Banu Abd-Shams, they are farsighted and cautious about all that is hidden from them. As for ourselves (Banu Hashim) we spend whatever we get and are very generous in offering ourselves in death. Consequently, those people are more numerous, more contriving and more ugly while we are more eloquent, well-wishing and handsome".
— Nahj al-Balagha, Hadith 120 
Jubayr ibn Mut'im (رضي الله عنه) narrated that he and Uthman ibn Affan (رضي الله عنه) went to Prophet Muhammad (صلى الله عليه وسلم) and said, "O Allah's Messenger! You have given (the Khums) to Banu Mutallib and left us although they and we are of the same kinship to you." The prophet said,
"Banu Mutallib and Banu Hashim are one and the same."
The Prophet did not give a share to Banu Abd Shams and Banu Nawfal. Ibn Ishaq related that Abd Shams, Hashim and Al-Muttalib were maternal brothers while their mother was 'Atika bint Murra and Nawfal was their paternal brother. 
Ibn Abbas (رضي الله عنه) was asked about the name 'Quraysh' by the Caliph Mu’awiya (رضي الله عنه) and he said, “It is a creature that resides in the sea. It eats and is not eaten. It is victorious and never loses.” Then he read the following verse of poetry:
وقريش هي التي تسكن البحر
“The shark is she who lives in the sea
بها سميت قريش قريشاً
because of it, the Quraysh were named Quraysh.”