Maoz Tzur is sung after the Menorah is lit in Ashkenazi Jewish households, every night of Hanukah. It's one of things that Jews tend to sing phonetically, without realising its meaning.
Maoz Tzur is written in the heavily allegorical and rhythmic language of the piyut (liturgical poem), a style most associated with medieval Ashkenaz - roughly what we now call Germany. It is thought to date from around the Thirteenth Century CE, and was composed by someone called Mordechai; we can tell this because an acrostic of his name is encoded in the first letters of its first five stanzas.
The commonly-known tune to Maoz Tzur is very Western, and it's been suggested that it's a corruption of German church music. An English translation, called Rock of Ages (NOT the Christian hymn of the same name) is popular in some parts of America, though it's largely unknown in Britain.
Maoz Tzur documents the troubles and escapes of the Jewish people from the Exodus from Egypt until the time of the Hanukah story. It originally had five stanzas; a sixth was probably added about 150 years later, which is more messianic and vengeful in its tone; not all families recite this verse. Heschelian cites a number of sources and reasons why the last verse may in fact be original and not a later addition, such as the three-letter word CHaZaK appearing in acrostic in the last stanza ( a common device) and the similarity of theme with the first verse. I'm not sure I agree with this analysis, primarily because the metre and rhythm is different.
A translation follows:
Sturdy rock of my salvation,
To you it is fitting to praise.
Perfect my house of prayer
And there a thanksgiving we will offer up.
At the moment the slaughter is prepared
For the barking enemy,
Then I will finish
In musical verse,
The Dedication of the Altar.
The first lines recall Psalm 31:2, and this stanza is an introduction of sorts to the theme of attack and redemption. The singer is Israel, the Jewish people, in the first person, and s/he is singing to God. The last words of the stanza are 'Hanukkat HaMizbeyach', the dedication of the Altar. This dedication is the origin of the name of the festival, Hanukah.
Bad things filled my soul
In grief my strength was lessened,
My life they embittered with hardship
With the bondage of the Calf-kingdom
And with his great hand
He took out the precious.
And all his children
Sank like a stone in the deep.
This stanza is about the Exodus. The references to Egypt as a calf follow Jer 46:20
To his holy dwelling he brought me,
But even there I wasn't quiet
And came an oppressor and exiled me
Because I had served strange ones,
And intoxicating wine I'd drunk.
Just as I had passed,
At the end of Babylon, Zerubbabel
At the end of seventy, I was saved
This stanza refers to the entire First Temple
period (approx 970 - 586 BCE
), where the predominant cycle was of the people of Judah
sinning and being punished, returning and being saved. Judah was exiled by Babylon, although only for seventy years, until the time of Zerubbabel.
To sever the tall cypress
Asked the Agagite, son of Hamdatha
Bit it was to him a trap and stumbling-block
And his arrogance was rested.
The head of the right-hand-one you lifted,
And the enemy, his name was erased
His many children and his possessions
On a tree you hanged.
This stanza is the story of Purim, as told in the book of Esther. Haman the Agagite wanted to kill Mordechai the Jew (not the same Mordechai as the author of Maoz Tzur!) who is a Benjaminite and compared poetically to a cypress tree.
Greeks gathered to me
Then, in the times of the Hasmoneans
And burst through the walls of my towers,
And defiled all the oils
And from the leftover of the flasks,
Was done a miracle to the roses
Sons of intelligence, eight days
Established song and rejoicing.
This is the verse that deals with Hanukah. It's pretty direct, except that it mentions the miracle of the oil, but not the Hasmonean War itself. In the original version of Maoz Tzur, this is the last verse.
Bare Your holy arm,
And bring closer the end, of salvation.
Avenge the revenge of your servants' blood
From the wicked state.
Because salvation is a long way from us
And there's no end to the days of evil
Fight off the Red one into the Shadows;
Establish for us the seven shepherds.
This verse is a plea for the End of Days, added after the Jews of Europe went through some particularly hard times. The 'Red one' is Edom, which symbolises evil in general and specifically Rome in Talmudic and Midrashic speak. Rome is the old Empire and the Church, so 'the red one' can be interpreted as Christianity. Heshelian brings some sources to suggest that 'the Red one' may even refer to a specific person, like Richard the Lionheart or Barbarossa.
Translation my own.
The Complete Artscroll Siddur provided some help when stuck, and some of the biblical references.
Suitable candidate for The Ninjagirls' quest