The 1979 Revolution in Iran is a very complicated event and there are lots of different interpretations both in academia and in the current Iranian political establishment. It's often highly politicised, with various groups supporting interpretations that support their political agendas.

The term 'Islamic Revolution' is itself contentious. The success of the movement against the Shah was rooted in the fact that it united all political factions in the country. The Islamists were concerned about the Shah's secularism, and his increased focus on Iran's pre-Islamic past in constructing a new, state-led nationalism. The middle class had a number of issues - massive state corruption, lack of political freedoms, competition with foreign goods/companies, and severe inflation. The lower classes were being squeezed by huge urbanisation and house price increase and again, a feeling that their Islamic identity was being marginalised by the Shah. Students and leftists took issue with the political repression and lack of democratisation/development of a civil society in light of the economic progress.

So, all these groups come out onto the streets and protest against the Shah, which eventually results in his removal, and he flees the country. You then have a vacuum, in the realisation dawns that no-one really knows what comes next. The plan was to remove the Shah, with little thought given to what comes after. The various factions, united in their protest, suddenly realise that they now have massive disagreements. For example, the students and leftists want a secular democratised state, whereas the Islamists, unsurprisingly, want one in which Islam plays a major role.

After the revolution, there is a public referendum on whether or not Iran was to be an Islamic Republic. The vast majority of people voted in the affirmative. It is important to note here that the detail of what constitutes an Islamic Republic was still not clear. However, Iran has always been an Islamic country, Islam plays a central role in the lives of most Iranians, in terms of social behaviour, morals, guidance, etc. Therefore when given a vote on the matter, an Islamic State made sense - after all, in the eyes of most, government was Islamic and should be Islamic. This does not mean that they supported all the subsequent policies of the Khomeini's government, rather, it is symbolic of the role and importance of Islam in Iranians' lives.

Sources; Ervand Abrahamian, Iran Between Two Revolutions Nikki Keddie, Modern Iran: Roots and Results of Revolution Said Arjomand, the Turban for the Crown.

As a follow-up question, why was there no concrete plan for post-revolution governance and if there was one why did western democracies and/or the Soviet Union fail to support it?