There has been some discussion on the Internet regarding the Park 51 community center (aka the "Ground Zero Mosque") as to whether the prayer space in the community center will be a mosque or not. This question has devolved into one even more basic: what is the difference between a mosque and a prayer space, such as one might find in a building that is not considered to be a mosque? This is my answer:
The distinction is somewhat hazy, but there is some distinction between mosques and other places in which we Muslims pray. Generally speaking, mosques are capable of holding more than 40 people (the minimum number of Muslims required for jumu'ah, the Friday congregational prayers), have a mihrab (the central niche that points the direction toward Makkah) and minbar (the pulpit from which the sermon is spoken from during jumu'ah), and normally performs all prayers with an imam present, including jumu'ah.
Here in SE Asia, we call a non-mosque facility a surau. A surau differs from a mosque in that it usually cannot fit 40 or more people in the facility*, may or may not have a mihrab, never has a minbar, and has no imams attached to the facility. They are used only for individual prayers and never for congregational prayers. (If two or more people happen to be at the surau at the same time, they may choose to pray together, but that's not considered congregational prayer.)
The Park51 facility may or may not be a mosque; it would at the very least be a surau. The key question from a Muslim perspective is, will jumu'ah be done there with the imam physically present? If yes, then it would be a mosque; if no, then it's only a surau.
* I've used several suraus over the years, the smallest of which was located in an Ikea store here in Singapore. That surau was big enough to fit in four people praying together at the absolute maximum.