Arabic is the official language of the 22 countries which form the Arab League: It’s the native language of over 200m people residing in this geographical region, which stretches from Southwest Asia to Northwest Africa and is also known as the Arab World. Arabic is also the liturgical language of over a billion Muslims around the world, as it’s the language in which the القرآن, Qur'an, the Holy Book of Islam, was revealed.
The "formal" Arabic language, known as Classical Arabic or الفصحى, Fus-ha, is the language in which the Qur’an is written and is considered to be the base of the syntactic and grammatical norms of the Arabic language. This Classical form of Arabic remains widely used by religious scholars and is taught in schools around the world. However, it is considered today more of a written language than a spoken one.
Modern Standard Arabic, or MSA, is similar but easier than Classical Arabic. It's understood across the Arab world and used by television presenters and politicians, for example, as well as to teach Arabic as a foreign language. You'll also find it in newspapers and works of modern Arabic literature.
In terms of "spoken" Arabic, there are many different dialects. An Arabic speaker from Iraq, for example, can find it almost impossible to understand a local Algerian, and vice versa - even though both individuals are speaking a particular form of Arabic dialect. However, both will be able to communicate in Modern Standard Arabic.