Taqiyya, or not showing their faith openly by means of pretense, dissimulation, or concealment, is a special type of LYING which is taught and used by Shi'a Muslims, cf. Sunni Muslims and Taqiyya. "Taqiyya" (or taqiyyah) is related to the terms "taqwa'" and "taqi'" - all have the root meaning of "guarding" something, in this case, the Islamic faith.
This practice, along with the practice of Kithman, or concealing their faith from non-Shi'as, were, and are many places today, a method of self-preservation for the Shi'a community. Historically, the Shiites have been in the minority and have been persecuted by Sunni Muslims who considered them heretics. Shi'as are often persecuted today in Pakistan and Afghanistan and Sunni-Shi'a violence is fairly common. Sunnis would often attempt to force Shi'as to curse the House of Ali - believing that no devout Shiite could commit such an act. As a result of this persecution, the idea of taqiyya emerged. In other words, if a Shi'a Muslim's life is in danger, he may lie as long as he holds true to Ali in his heart.
Shi'as believe that the origin of this line of defence comes from the Qur'an. When Moses returned from the mountain and saw his people worshiping the golden calf, he was understandably angry and asked his brother Aaron why he allowed such a terrible sin to be committed. The Qur'an tells us
This verse is important because, since all Muslims believe that Aaron is a Prophet, none would criticize him for cowardice.
A more specific justification for taqiyya by the Shi'as is the instance when 'Ammar ibn al-Yasir (one of the companions loyal to 'Ali and considered to be one of the first Shi'a) was detained and tortured by infidels. He renounced his faith in order to escape and immediately went to Muhammad and repented. 'Umar suggested that he be put to death for apostasy, however, Muhammad said that it was better for him to renounce his faith with his lips (while still believing in his heart) than to be burned to death by the infidels.
This account is surprising considering how much emphasis the Qur'an places on martyrdom. Today, many Sunnis criticize 'Ammar for his actions and there is a significant difference of philosophy between Sunnis and Shi`a which creates this dilemma. The Sunnis believe that human beings have little or no free will, while the Shi`a believe that humans enjoy a great deal of free will.
To a Sunni, God decides how, and when, one is going to die and what is going to happen to all people - both believers and unbelievers. Therefore, it makes little difference what decisions one makes - everything is in God's hands, and it is not right to outwardly deny the faith in order to escape torture or death.
By contrast, the Shi'a believe that life is a gift from God and like any gift from God, should be preserved and not squandered. Anything that one can do to save one's life should be done, even if it is contrary to God's laws. In a life-threatening emergency, self-preservation, and the preservation of the faith take precedence over obedience to the shari'ah - in fact, this kind of preservation in such situations would be considered obedience to the shari'ah.
Taqiyya is to be practiced only when one fears for one's life, the lives of one's family members, or for the preservation of the faith. In those situations, according to most Shi`a jurisprudents, taqiyya is required!
Some Shiite Traditions promoting taqiyya are
Zararah narrates that I asked a certain question to Imam Baqar (R). He gave me its answer. Another person then asked the same question and the Imam gave him a different answer. Later a third person asked the same question, but the Imam's answer this time was different from the previous two answers. I then asked him: "O, the son of the Messenger (S)! The two persons who just came here to ask you questions were from Iraq and were Shias, yet you gave them contradictory answers". The Imam then answered: "O Zararah! This is good for me as well as for you and this will help us survive and prosper". (Ft. #2 Ibid, p.37)
For more information on this topic, please read this article and this linked section of Relation of Shi'a Theology to the Qur'an.
Shia Encyclopedia entry: Taqiyya
Sunni Muslims and taqiyya
However, although taqiyya is usually seen as a Shia doctrine only, it is practiced and taught also by Sunni Muslims, cf. the discussion of friendship with unbelievers in the entry on FRIENDS. Here just one quotation from a Sunni website, Islam Q&A (www.islam-qa.com), advising in regard to making friends with non-Muslims:
"Let not the believers take the disbelievers as Awliyaa' (supporters, helpers) instead of the believers, and whoever does that, will never be helped by Allaah in any way, except if you indeed fear a danger from them" [Aal 'Imraan 3:28]
This verse explains all the verses quoted above which forbid taking the kaafirs as friends in general terms. What that refers to is in cases where one has a choice, but in cases of fear and TAQIYYAH it is permissible to make friends with them, as much as is essential to protect oneself against their evil. That is subject to the condition that one's faith should not be affected by that friendship and the one who is behaves in that manner out of necessity is not one who behaves in that manner out of choice.
Shaykh Muhammad al-Saalih al-'Uthaymeen (may Allaah have mercy on him) was asked about the ruling on mixing with the kuffaar and treating them kindly hoping that they will become Muslim. He replied:
Undoubtedly the Muslim is obliged to HATE the enemies of Allaah and to disavow them, because this is the way of the Messengers and their followers...
Based on this, it is not permissible for a Muslim to feel any love in his heart towards the enemies of Allaah who are in fact his enemies too...
But if a Muslim treats them with KINDNESS and gentleness in the hope that they will become Muslim and will believe, there is nothing wrong with that, because it comes under the heading of opening their hearts to Islam. But if he despairs of them becoming Muslim, then he should treat them accordingly. This is something that is discussed in detail by the scholars, especially in the book Ahkaam Ahl al-Dhimmah by Ibn al-Qayyim ... (Question #59879: What is meant by taking the kuffaar as friends? Ruling on mixing with the kuffaar; bold and capital emphasis ours)
Further discussion: Sunni Muslims and Taqiyyah
See also the entries LYING and DECEPTION.