Besides being an Arabic phrase that means "God is the greatest", Allahu Akbar, is the beginning to the Azan, a common salutation, and the name of the national anthem of the Socialist People's Libyan Arab Jamahiriya.

First off, the salutation is said at the beginning of every Islamic prayer. Imam Sultan Muhammad Shah (who also goes by the name Aga Khan III) says,

"Consider for example the opening declaration of every Islamic prayer: "Allah-o-Akbar". What does that mean? There can be no doubt that the second word of the declaration likens the character of Allah to a matrix which contains all and gives existence to the infinite, to space, to time, to the Universe, to all active and passive forces imaginable, to life and to the soul."

Allahu Akbar, the national anthem of Socialist People's Libyan Arab Jamahiriya, was adopted in 1969 with the rise to power of Muammar Qaddafi. Allahu Akbar was written by Abdalla Shams El-Din, and was set to music written by Mahmoud El-Sharif. The lyrics below are in transliterated Libyan Arabic, followed by the English translation.

Allahu Akbar
Allahu Akbar
Allahu Akbar Fauqua Kaidi L'mutadi
Allahu Lilmazlumi Hairumu'ayyidi
Allahu Ana Bilyaqini Wabissilahi Saaftadi
Baladi Wanuru L-haqqi Yastau Fi Yadi
Qulu Mai
Qulu Mai
Allahu Allahu Allahu Akbar
Allahu Fauqa L-mutadi

Ya Hadihi Ddunya Atilli Wa 'Smai
Gaisu L-aadi Ga'a Yabgi Masrai
Bil-haqqi Saufa Fa-saufa Afnihi Mai.

Qulu Mai L-wailu Lil-mustamiri
Wa Llahu Fauqa L-gadiri L-mutagabbiri
Allahu Akbaru Ya Biladi Kabbiri
Wa-hudi Binasiyati L-mugiri Wa-dammiri

And now for the English translation:

God is greatest!
God is greatest!
He is above plots of the aggressors,
And He is the best helper of the oppressed.
With faith and with weapons I shall defend my country,
And the light of truth will shine in my hand.
Sing with me!
Sing with me!
God is greatest!
God is greatest!
God, God, God is greatest!
God is above the aggressors.

O world, look up and listen!
The enemy's army is coming,
Wishing to destroy me.
With truth and with my gun I shall repulse him.

And should I be killed,
I would kill him with me.
Sing with me -
Woe to the Imperialists!
And God is above the treacherous tyrant.
God is greatest!
Therefore glorify Him, O my country,
And seize the forehead of the tyrant
And destroy him!

Translation obtained (with permission) from an ex-node. Some other info was gathered from