Avinu Malcaynu is a Jewish prayer of repentance, and as such is said every day from Rosh Hashanah until Yom Kippur, the period known as the 10 days of repentance, when Jews look back on the previous year and forward to the coming year, and ask man and G-D for forgiveness for any sins they have committed in the previous year. It is also said on most of the other Jewish fast days in a slightly modified form. It is not said on Shabbat, except for the last service on Yom Kippur.
The prayer consists of 44 verses, each one beginning with the words "Avinu Malcaynu" - "Our Father, Our King". The first verse is perhaps the simplest, and sums up the entire prayer. "Avinu Malcaynu, Chatanu L'fanechah" - "Our Father, Our King, We have sinned before you". Note that all Jewish prayers of repentance are in the plural, as we are judged as a people.
The prayer has a key section in the middle where we ask to be inscribed in various "books". This is based on the idea that between Rosh Hashanah and Yom Kippur, G-D writes down every Jew's name in a book based on how they have behaved the previous year, and what will happen the next year. The five books referred to are:
- The Book of Life and Good
- The Book of Redepmtion and being Saved
- The Book of Success
- The Book of Good Luck
- The Book of Forgiveness
These five lines are modified depending on when the prayer is being recited.
- On other fast days throughout the year - Our Father, Our King, Remember us for Life and for Good
- From Rosh Hashanah until Yom Kippur - Our Father, Our King, Inscribe us in the Book of Life and Good
- In the Neilah service, the very end of the Yom Kippur prayers - Our Father, Our King, Seal us in the Book of Life and Good
Of course all five verses are modified appropriately. The difference with the last service on Yom Kippur is that at this time, G-D is making his final decision as to the sort of year we will have ahead of us, so we have one final request not just to write us in the books, but to seal them as well with us written in them.
The last line of the prayer is usually sung out loud to a stirring melody - this is probably the part of the prayer stylee is referring to. Its approximate translation is Our Father, Our King, be gracious to us and answer us, for we have no (good) deeds. Deal with us with Charity and Kindness, and Redeem us. A fitting end to the holiest day of the Jewish year.