Although the Kaddish contains no reference to the dead, it has been recited by mourners for many centuries. The tradition of the mourner's Kaddish began with the following incident: Once, while walking, Rabbi Akiva met a man who had died some time before and was suffering the torments of Purgatory. He pleaded with Rabbi Akiva to go to his home town and teach his son to recite the Kaddish and Borechu, for this would save him from the terrible punishments. Rabbi Akiva and his Court then instituted the practice of mourners reciting the Kaddish, for until then it had been limited to the Chazzan's reciting it only after the services or after a sermon (See Tana D'vei Eliyahu Zuta, 17: Zohar Parshas Noach).
יִתְגַּדַּל וְיִתְקַדַּשׁ שְׁמֵהּ רַבָּא Exalted and sanctified be His great Name
בְּעָלְ֒מָא דִּי בְרָא in the world which He created
כִרְעוּתֵהּ according to His will
וְיַמְלִיךְ מַלְכוּתֵהּ and may He rule His kingdom
וְיַצְמַח פּוּרְ֒קָנֵהּ bring forth His redemption
וִיקָרֵב (קֵץ) מְשִׁיחֵהּ and hasten the coming if His Messiah
בְּחַיֵּיכוֹן וּבְיוֹמֵיכוֹן in your lifetime and in your days,
וּבְחַיֵּי and in the lifetime
דְכָל בֵּית יִשְׂרָאֵל, of the entire House of Israel,
בַּעֲגָלָא וּבִזְמַן קָרִיב speedily and in the near future—
וְאִמְרוּ אָמֵן: and say Amein.
יְהֵא שְׁמֵהּ רַבָּא מְבָרַךְ May His great Name be blessed
לְעָלַם וּלְעָלְ֒מֵי עָלְ֒מַיָּא: forever and for all eternity.
יִתְבָּרַךְ וְיִשְׁתַּבַּח Blessed and praised,
וְיִתְפָּאַר וְיִתְרוֹמַם וְיִתְנַשֵּׂא glorified, and exalted and uplifted,
וְיִתְהַדָּר וְיִתְעַלֶּה וְיִתְהַלָּל honored and elevated and extolled
שְׁמֵהּ דְקוּדְשָׁא, בְּרִיךְ הוּא be the Name of the Holy One, blessed is He;
לְעֵֽלָּא (בעשי"ת וּלְ֒עֵֽלָּא מִכָּל) above (Ten Days of Penitence: far above)
מִן כָּל בִּרְכָתָא וְשִׁירָתָא, all the blessings and hymns,
תֻּשְׁבְּחָתָא וְנֶחֱמָתָא, praises and consolations
דַּאֲמִירָן בְּעָלְ֒מָא, וְאִמְרוּ אָמֵן, which we utter in the world—and say Amein.
יְהֵא שְׁלָמָא רַבָּא מִן שְׁמַיָּא May there be abundant peace from heaven
וְחַיִּים and life
עָלֵֽינוּ וְעַל כָּל יִשְׂרָאֵל for us and for all Israel,
וְאִמְרוּ אָמֵן: —and say Amein.
עוֹשֶׂה שָׁלוֹם He Who makes peace
(בעשי"ת הַשָּׁלוֹם) (Ten Days of Penitence: the peace)
בִּמְרוֹמָיו in His high heavens
הוּא יַעֲשֶׂה שָׁלוֹם may He, make peace
עָלֵינוּ וְעַל כָּל יִשְׂרָאֵל for us and for all Israel,
וְאִמְרוּ אָמֵן and say, Amen.