I am reminded of the philosopher Ludwig Wittgenstein's observation:
"One thinks that one is tracing the outline of the thing's nature over and over again, and one is merely tracing round the frame through which we look at it."I suggest that this is how a lot of people form their understanding of mosques — they look at a mosque and think 'Islamic church', because a church is what they are familiar with. It is the frame they are looking through.
Rabbi Bretton-Granatoor presented a sermon for the 9/11 anniversary in which he stated that "a mosque should be a place of peace, prayer and study", as if this were a self-evident truth. But is it? Or was he in fact describing his ideal synagogue?
To understand what a mosque is in Islam, we need to grasp that Islamic practice and belief is based upon the example and teaching of Muhammad. What determines the function of a mosque — from a religious perspective — is how Muhammad used mosques. The question "What is a mosque?" begs the question "How did Muhammad use mosques?"
What needs to be kept in mind is that Islam does not separate faith from politics. This is becauase Muhammad combined in himself the offices of chief priest, head of state, general of the army, and chief justice. Just as he combined all these functions, so in Islam, the mosque can be a site for political, military, religious and legal activities. It can be a parliament, military parade ground, church and a court. And during Muhammad's life time, mosques were at various times, all these things. This is all explained in the handy booklet The Mosque Exposed by Sam Solmon and E Alamaqdisi, who give examples of Muhammad using mosques for such diverse purposes.
But let's consider what a significant contemporary scholar has said on the subject. Yusuf Al-Qaradawi is an influential person. He is no lightweight or fringe-dweller. A trustee of the Oxford University Centre for Islamic Studies, he was named by Foreign Policy Magazine as number 3 in a poll to determine the top 20 public intellectuals in the world today.
In 2006 Al-Qaradawi produced a fatwa (a religious ruling) to answer the question: "Is is permissible to use a mosque for political purposes?" (The Arabic text can be found here.) (Apparently this was a revision of an earlier fatwa, issued in 2001.)
Al-Qaradawi's answer was 'Yes it is,' and included the following remarks:
The mosque at the time of the Messenger of Allah [Muhammad] was the center of the activities of the Muslim community as a whole: it was not just a house of worship and prayer, but included worship, a university for science, a forum for literature, and a parliament for consultation ... it was used by delegations from various places in the Arabian peninsula to meet with the prophet [Muhammad], and it was the place where he gave his sermons and guidance in all religious, social and political aspects of life.
In the life of the prophet there was no distinction between what the people call sacred and secular, or religion and politics: he had no place other than the mosque for politics and other related issues. That established a precedent for his religion. The mosque at the time of the prophet was his propagation center and the headquarters of the state.
This was also the case for his successors, the rightly guided Caliphs: the mosque was their base for all activities political as well as non-political.
... Politics as a science is one of the best disciplines, and as a practice and career it is the most honorable. The surprising thing is that it is politicians, who are totally immersed in it [politics] from the top of their heads to the soles of their feet, who are inquiring if the mosque should embark on and leap into political affairs. Politics in itself is neither vice, nor evil, according to Islam. ... For Muslims it is part of our religion: doctrine and worship constitute a system for the whole of life.
... It must be the role of the mosque to guide the public policy of a nation, raise awareness of critical issues, and reveal its enemies.
From ancient times the mosque has had a role in urging jihad for the sake of Allah, resisting the enemies of the religion who are invading occupiers. That blessed Intifada in the land of the prophets, Palestine, started from none other than the mosques. Its first call came from the minarets and it was first known as the mosque revolution. The mosque's role in the Afghan jihad, and in every Islamic jihad cannot be denied.
The last point about jihad is an important one. It explains why time and again intelligence agencies have established links between jihadis and particular mosques, where the faith and intentions of young men have been so nurtured that they were ready and willing to undertake jihad for the sake of Allah.
There are reported to be 40,000 to 50,000 mosques in the United States, but there is not a single church in Saudi Arabia. The issue for municipal planning authorities to consider, when they receive a request to issue a permit for a mosque, is how can they know what kind of facility this will turn out to be? No doubt there are many mosques which are simply places of private devotion and public worship. But, according to Yusuf Al-Qaradawi, there is much more to a mosque than this.
 Wittgenstein, Ludwig. Philosophical Investigations. Prentice Hall, 1973. p. 114.