could you please tell me what is “by their Father” means

The kaddish is a very important prayer which is recited during the dauly parayers neumoros times

The central theme of the Kaddish is the magnification and sanctification of G-d‘s name.

As the kaddish begins
“Yitgaddal veyitqaddash shmeh rabba” “Exalted and sanctified be His great name^“”

With there being four or five different types of kaddish

With the primary ones being

• Ḥaṣi Qaddish (חצי קדיש ‘Half Kaddish’) which is primary a braker in the middle of prayer


• Qaddish Shalem(קדיש שלם) or Qaddish Titkabbal (קדיש תתקבל) – literally “Complete Kaddish” or “Whole Kaddish” which is a special prayer said at every minyan that g-d should accept our prayer


• Qaddish de Rabbanan(קדיש דרבנן ‘Kaddish of the Rabbis’) or Qaddish ʿal Yisraʾel (קדיש על ישראל) which is recited after learning mishnayot or braisot


• Qaddish Yatom(קדיש יתום) or Qaddish Yehe Shlama Rabba (קדיש יהא שלמא רבא) – literally ‘Orphan’s Kaddish’, although commonly referred to as Qaddish Avelim (קדיש אבלים), the ‘Mourner’s Kaddish’ which is primarly said by mourners

Here is a very famous story which illustrates the importance of the mourners kaddish:

 

• Rabbi Akiva, once saw a man struggling under a heavy load of wood. Rabbi Akiva stopped the man and said, “Why must you do this difficult work? If you are a slave and this labor is forced upon you, I will redeem you from your master and set you free. And if it is because you are poor and you must earn a living this way, I will make you rich.” Frightened, the man responded, “Please let me go and do not detain me, so as not to anger those who are in charge of me.”


• The man’s reply puzzled Rabbi Akiva, who asked, “Who are you and what is this all about?” To this, the man replied, “I am one of those unfortunate souls condemned to the agonies of hell-fire, and every day I am sent to bring my own wood for my own torment.” “Is there then no way for you to be relieved of this suffering?” asked Akiva. “Yes,” the man answered. “I heard that if my little son, whom I left behind, were to say in public, ‘Yitgadal veyitkadash‘ and the others would answer, ‘Yehei Shemei rabba mevorakh,’ or if he were to say, ‘Barekhu et Adonai hamevorakh,’ and the congregation would answer, ‘Barukh Adonai hamevorakh l’olam va-ed,’ I would be set free from this judgment.”


• Rabbi Akiva then asked the man for all the relevant details and promised to locate his child and teach him Torah so that he could stand in front of the congregation and say Yitgadal in praise of God. Akiva found the child and taught him Torah, the Sh’ma, the Amidah, and Grace After Meals and prepared him to stand before the congregation to recite Yitgadal. As soon as the boy did this, the father’s soul was delivered from its judgment and permitted its eternal rest. The man then appeared to Rabbi Akiva in a dream and thanked him: “May it be God’s will that you rest in peace, for you made it possible for me to be at peace.”


• In the kaddish we say “קדם אבוהון דבשמיא” before their father in heaven, which refers to g-d as it is written the holy books that one of the types of relationship between us the Jewish people and g-d is the relationship of a father and son as the verse says “בני בכורי ישראל”  “my first born son Israel” , and just like a father and son are always connected and in every situation the father is caring and concerned for his child, so to g-d is always caring and concerned for the Jewish people and as we stated  during  the Rosh Hashono prayers that g-d should have mercy upon us like a father has for his children


• In light of this you can understand why in this important prayer we refer to G-d as a father of the Jewish people