Lead Tidbit
Avinu Malkeinu, please...
The story is quoted from the Gemara that during the period of the Tana'im, there was once a fast declared because of severe drought. As is/was the practice, Mincha was held in the public square rather than in the shul, and one of the great Tana'im led the davening. When he finished the special Amida, including additional brachot because of the special fast, it was felt that his prayers had not succeeded in moving G-d, so to speak, to respond favorably to the pleas of His people. Rabbi Akiva then approached the Amud and Aron and said: Avinu Malkeinu, our Father and King, we have no other King but You, Avinu Malkeinu, for Your sake, have mercy on us.

Continues the Gemara (Taanit 25b), it started to rain. Avinu Malkeinu evolved from that time on to the present list of petitions that we have in our Siddur. Some sources say that the original text of Avinu Malkeinu closely followed the middle brachot of the weekday Amida. A comparison of the list of Avinu Malkeinu sentences and the brachot of the Amida will bear this out.
We say Avinu Malkeinu twice daily during Aseret Y'mei T'shuva (except for Shabbat and Erev Shabbat afternoon). On Yom Kippur, it is said 3, 4, or 5 times (customs vary).

Some of the lines of Avinu Malkeinu ask G-d for specific things, and others ask for Him to be merciful and respond favorably to our requests, for His sake and on behalf of those Jews who have lost their lives sanctifying His name.

There are many things to say on this topic. Let's say just this: Many of our special prayers for Yamim Nora'im, as well as our regular daily prayers, ask many things of G-d. If we want Him to respond favorably, we should at least say the petitions with understanding of what we are asking for and with sincerity in our hearts. This must apply to Avinu Malkeinu, the Amida it is based on, and every other prayer of request, praise, thanks, acknowledge- ment... and every bracha we say.

Sort of a continuation...
The prayer Avinu Malkeinu came into existence because of a situation when a full Amida, recited by a Tana of highest regard, failed to produce favorable results, and Rabbi Akiva's impassioned words pierced the curtain that was blocking the prayers of the People of Israel and DID produce results.

We are going to be saying Avinu Malkeinu and a lot of other T'filot on Yom Kippur. Simply put, without kavana, sincerity, feeling... they too might not produce favorable results. With strong kavana, they stand a good chance. If it is results that we are hoping and praying for, then we have work to do. Let's do it.

Emphasis on the plural - let's. It is well- known that are prayers were purposely composed using plural. Avinu Malkeinu - not Avi, Malki. S'LACH LANU, forgive US, not S'LACH LI. What gives us the right and the power to pray on behalf of others, as we plead before G-d for our own forgiveness? It is the commitment that each Jew has - or should have - towards our fellow Jews.

Some people have the custom of saying the following before they daven:
HAREINI M'KABEL ALI MITZVAT ASEI SHEL V'A'HAVTA L'REIACHA KAMOCHA

I hereby accept upon myself the mitzva of loving my fellow Jew. This allows me to daven for all of Klal Yisrael, and not just for myself. It converts a basically "between the Jew and G-d" kind of mitzva into one that is very much BEIN ADAM L'CHAVEIRO, between the Jew and his fellow.
This is an important step in our davening that changes it from self- centered to include other individuals, and all of B'nei Yisrael.

This awareness should lead to a general improvement in the area of interpersonal mitzvot.

It's all connected. Paying attention to the correct pronunciation of a word in the davening, or the proper syllable to accent leads (should lead) to better understanding of davening. That, in turn leads (should lead) to a greater appreciation of Whom we daven to. And on behalf of whom we daven. That leads (should lead) to an improvement in the performance of all mitzvot and a stronger shunning of sinful and improper behavior. And it should takes us on the path to real T'SHUVA.

As Tevye was wont to say: From our lips (and hearts) to G-d's ears (and heart, so to speak). G'MAR CHATIMA TOVA