The word adhaan in Arabic means announcing or proclaiming. 

In sharee’ah terminology it means announcing the time of prayer. 

Majmoo’ al-Fataawa, 22/72. 

The adhaan was prescribed at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him) in Madeenah, after a dream seen by one of the Sahaabah. 

It was narrated that ‘Abd-Allaah ibn Zayd ibn ‘Abd Rabbihi said: “When the Messenger of Allaah (peace and blessings of Allaah be upon him) decided to use a bell, he did so reluctantly because that was like what the Christians did. Then at night whilst I was sleeping, a man walked around me [in my dream], wearing two green garments and carrying a bell in his hand. I said to him, ‘O slave of Allaah, will you sell the bell?’ He said, ‘What will you do with it?’ I said, ‘I will call (the people) to prayer.’ He said, ‘Shall I not tell you of something better than that?’ I said, ‘What is it?’ He said, ‘Say: ‘Allaahu akbar…’ (to the end of the adhaan). The following morning I came to the Messenger of Allaah (peace and blessings of Allaah be upon him), and told him what I had seen. He said, ‘It is a true dream, in sha Allah. Go out with Bilaal to the mosque and teach it to him, for he has a more melodious voice than you.’ I went out with Bilaal to the mosque, and I started teaching him the words and he was calling them out. ‘Umar ibn al-Khattaab heard the voice from his house and came out dragging his lower garment and saying, ‘O Messenger of Allaah! By Allaah, I saw the same (dream) as him.’ The Messenger of Allaah (peace and blessings of Allaah be upon him) said, ‘To Allaah be praise.’” 

Narrated by al-Tirmidhi, 189; Abu Dawood, 499; Ibn Maajah, 706

This hadeeth was classed as saheeh by Ibn Khuzaymah, 1/189; Ibn Hibbaan, 4/572; al-Albaani in Tamaam al-Minnah, p. 145. 

The adhaan is fard kifaayah (a communal obligation). The people of every town must have someone among them who can give the call to prayer so that the people may be informed that the time for prayer has come. 

The scholars of the Standing Committee said: 

The adhaan is fard kifaayah (a communal obligation) in a town, and the same applies to the iqaamah. If a person starts to pray without the adhaan or iqaamah, whether out of forgetfulness or ignorance, or for some other reason, the prayer is still valid. The same applies if the muezzin forgets the phrase al-salaatu khayrun min al-nawm (prayer is better than sleep) in the adhaan for Fajr prayer; the prayer is still valid even if there is still time left after he has finished his prayer (i.e., he does not have to repeat it). And Allaah is the Source of strength; may Allah send blessings and peace upon our Prophet Muhammad and his family and companions . 

Fataawa al-Lajnah al-Daa’imah, 6/54 

There are many ahaadeeth which speak of the virtues of the adhaan, such as that narrated by al-Bukhaari, 609, from Abu Sa’eed al-Khudri, which says that the Prophet (peace and blessings of Allaah be upon him) said: “No jinn or human hears the voice of the muezzin for as far as it carries, but he will bear witness for him on the Day of Resurrection.” 

And Allaah knows best.