Labbayk means to answer in the affirmative, to agree with and accept an invitation, an acceptance accompanied with honor, respect and praise. This term was originally "Labbayna" plus "Lak", and turned to "Labbayk" through combining the two words into one (Idghaam).
This term (which constitutes the main part of the Talbiyah of Ihram in Hajj) is one of the wajib acts of Hajj; by saying it, one becomes a Hajj pilgrim and enters the state of Ihram.
Regarding the reason behind why it is wajib in the beginning of the rites of Hajj, one must say that this matter has been mentioned in a hadith by Imam Kadhim (AS). He has been reported saying: "When the people become Muhrim (enter the state of Ihram), Allah calls unto them saying: O my servants! The same way you have become Muhrim for me, I have made the Hellfire haram for you. Saying "Labbayk Allahumma Labbayk" is actually an answer to God in return to what He has said." Also, it has been mentioned in other hadiths that this term is an answer to the Quranic verse addressing Prophet Ibrahim to tell the people to perform Hajj. By saying this, the people are answering the call of God to perform Hajj.
This term has also been mentioned in the supplications of the first takbirs of prayer as well. It has also been mentioned in two supplications of the Sahifah Sajjadiyyah. In these cases, it means to answer and accept the call of God to prayer, supplication, etc.
 Bustani, Fo'ad Afraam, Farhange Abjadi, Mahyar, Reza, Islamic Press, Tehran, second edition, 1375 (solar).
 Muqri Fuyumi, Ahmad ibn Muhammad, Al-Misbah al-Munir fi Gharib al-Sharh al-Kabir li al-Raafi'i, vol. 2, p. 547, Daar al-Radhiyy Press, Qum, first edition, no date.
 Talbiyah, means to say "Labbayk", the special phrase of which is said in Hajj is: Labbayk Allahumma Labbayk, Labbayka Laa Sharika Labbayk.
 Bahjat, Muhammad Taqi, Manasik Hajj va Umrah, p. 90, Office of Ayatullah Bahjat, Qum, third edition, 1424 AH.
 Shaykh Hurr Amili, Wasa'il al-Shia, vol. 12, p. 375, Aal al-Bayt Institute, Qum, first edition, 1409 AH.
 Ibid, p. 377.
 It is mustahabb to say six takbirs in the beginning of the prayer which totals to seven when added to he takbir of Ihram that begins the prayer. There are special supplications that are mustahabb to be said in between these takbirs. The following is one of these supplications: "لَبَّیْکَ وَ سَعْدَیْکَ وَ الْخَیْرُ بَیْنَ یَدَیْکَ وَ الشَّرُّ لَیْسَ إِلَیْکَ وَ الْمَهْدِیُّ مَنْ هَدَیْت... "
 Sahifah Sajjadiyyah, Supplications 16 and 51.