We are supposed to have deep kavvanah while praying and for different mitzvot. The haftarah read on the first day of Rosh haShanah has in it Hannah's Prayer. enters the sanctuary at Shiloh and prays earnestly and is accused by the High Priest of being drunk. She responds that she isn't drunk but has poured out her soul to HaShem. The High Priest tells her to go in peace.
This is how we are supposed to pray. The reading teaches it very well. The reading teaches us other things as well. In Modern Orthodox and ultra-Orthodox shuls, women are separated from the men and their voices are not supposed to be heard. But from Hannah's prayer and they way the High Priest acted toward her, it seems that women were not only supposed to be in the sanctuary but their voices were to be heard in prayer. Why else would he consider her to be drunk? She wasn't acting in the proscribed manner and gained the High Priest's attention. Not only did the High Priest question her directly, he also learned a valuable lesson in kavvanah.
It also teaches that women were expected to be heard during prayers. During the long and tragic Diaspora, Jews adopted many customs from the countries they found themselves in. From what I've read, the custom of separating men and women during prayer services started some time in the 1100s. To me, it is a harmful custom and teaches that the efforts of women to approach HaShem are some how less than a man's. The Torah teaches us different. Time and again, it has been the actions of a woman that teaches us much. We have the examples of Sarah, Rachel, Leah, Rebecca, Miriam, Ruth, Deborah, and Hannah to show us. Sarah laughed. Miriam sang and danced. Deborah judged. Ruth words are some the most stirring words on the faith of the Jewish people: for whither thou goest, I will go; and where thou lodgest, I will lodge; thy people shall be my people, and thy God my God; 17 where thou diest, will I die, and there will I be buried; the LORD do so to me, and more also,
The megillah of ruth is read on Shavuot. It is fitting that it is so. When Moses led Israel to Mount Horeb, the voices of men and women proclaimed together that they accept and will do the mitzvot.
Because of the kavvanah of Hannah, the prophet Samuel was born. Because of the love of Ruth, King David was born. If the voices of these women had been silenced, what would have been the outcome?