The name Allah (الله) is the Arabic term for the God of Islam. This theonym is likely a contraction of Arabic Al-'ilāh (ال إِله), which means "the god". It is thus related to the Hebrew term Eloh(-im).
In Islam, Allah is the personal name of God and comprises all of the 99 Names of God in Islam. When a Muslim refers to Allah, he thinks of God as being One, Creator, Owner, Sustainer, and Almighty. In Arabic, the name is composed of four letters, ا ل ل ه (or Alif, Lam, Lam, Ha) which when brought together make الله. Arab Christians often incorrectly use this name simply as a generic term "god". (The actual generic word for "god" is simply 'ilāh, though due to the strong association of Arabic with Islam this word is rarely used in modern speech.) These Christians do maintain a belief in the traditional Christian Trinity, however, and believe that Allah consists of the Father, Son and Spirit.
Christianity and Judaism
As noted, the name Allah is used by Arab Christians throughout the Middle East. It is also used by Arabic Jews, especially those residing in Yemen.
Possible Early Use
It is a matter of contention as to whether the name Allah came into use only with the foundation of Islam, or whether it is a reuse of a title of the main pagan god of pre-Islamic Mecca; Hubal, god of the Moon. Muslim scholars have offered reasonable refutations of this allegation, but some Christian groups have offered counter-refutations that are seemingly logical as well. Whether the allegation is true is unknown.
Takbeer (Glorification of God)
Takbeer (تَكْبِير) (Glorification of God), is the common way Muslims give glory to God. The wording used is Allahu-Akbar "الله أكبر", which is translated as "God is greater". It is a very common practice in Islam and is essential to the Islamic call of prayer (Athan).