Rambam in MN1:54 explains the meaning of this response –
“Although Moses was shown "all His goodness," i.e., all His works, only the thirteen Midot are mentioned, because they include those acts of God which refer to the creation and the government of mankind, and to know these acts was the principal object of the prayer of Moses.”
In our search for God, we look at nature. We are awed by the intelligence we perceive in the laws of nature and through them, we start to get an understanding of God. We now have to translate what we learned into practical actions. Rambam continues –
“Whenever any one of His actions is perceived by us, we ascribe to God that emotion which is the source of the act when performed by ourselves, and call Him by an epithet which is formed from the verb expressing that emotion. We see, for example, how well He provides for the life of the embryo of living beings. How He endows with certain faculties both the embryo itself and those who have to rear it after its birth, in order that it may be protected from death and destruction, guarded against all harm, and assisted in the performance of all that is required [for its development]. Similar acts, when performed by us, are due to a certain emotion and tenderness called mercy and pity. God is, therefore, said to be merciful: e.g., "Like as a father is merciful to his children, so the Lord is merciful to them that fear Him" (Ps. 103:13).”
The goal is the survival of the species and thus the individual that makes up the group. As part of the system, a child is born helpless and is provided with protection - the womb while it is an embryo, the parent’s love and protectiveness after it is born until the child grows up and fends for himself.
“The governor of a country, if he is a prophet, should conform to these attributes… At times and towards some persons he must be merciful and gracious, not only from motives of mercy and compassion, but according to their merits”.
A leader that is also aware of how God created the world where everything is consequential understands that he has to emulate Him in his own governance. Just like God is selfless, after all, He is uniquely non-contingent and therefore there can be no reciprocity, so too must a leader act selflessly. The thirteen attributes stand for all the ways that a person who gets to a certain level of understanding should try to emulate God. The Gemara Rosh Hashana 17b reads -
א"ר יוחנן אלמלא מקרא כתוב אי אפשר לאומרו מלמד שנתעטף הקב"ה כשליח צבור
והראה לו למשה סדר תפלה אמר לו כל זמן שישראל חוטאין יעשו לפני כסדר הזה
ואני מוחל להם
The verse the Gemara is dealing with is in Shemot 34:6 –
ו וַיַּעֲבֹר יְהוָה עַל-פָּנָיו, וַיִּקְרָא, יְהוָה יְהוָה, אֵל רַחוּם וְחַנּוּן--אֶרֶךְ אַפַּיִם, וְרַב-חֶסֶד וֶאֱמֶת
There are two ways of interpreting this verse. Hashem passed in front of Moshe and Moshe declaimed Hashem, Hashem … or alternatively Hashem declaimed – Hashem…. Rabbi Yochanan chooses the latter interpretation namely, that God showed Moshe His attributes of action. Rabbi Yochanan is teaching us the meaning of prayer. It is not just a formulaic plea; it is a realization that we have to act in a certain way for things to improve. Prayer is the contemplation that leads to emulating God. It is not Moshe petitioning God with a formula, but rather Moshe “seeing” God’s ways, contemplating them with the goal of emulating them. Rambam in a responsa (Blau 267) says that he never declaimed the verse during the Krias Hatorah on a Ta’anit the way the popular custom is. He then continues to say that the correct way to read the verse is that God said, and that no one ever interpreted it differently.
התשובה אלו הקריאות כולן אין עיקר להן, ולא נזכרו כלל בדבר מדברי רז"ל, והקרוב אצלי, שהם מנהגי חזנין שנתפרסמו. אבל אני לא קראתי אותן מעולם, משום שאיני יודע לזה עיקר, והוא דבר שאין לו מובן ברור,
ושהשם הראשון אינו מן השלש עשרה מדות, הרי זה דבר נכון, לא שמעתי מעולם מי שחלק על זה
ופשוטו של מקרא מורה על זה, לפי שהוא יתעלה, אמר וקראתי בשם ה' לפניך, אחר כך סיפר קיום זאת ההבטחה, והזכיר, שה', יתעלה שמו, קרא ה', אל, רחום, וחנון וגו' ,
The contemplation of these attributes is meant to remind us that we have a role to play in God’s world as human beings. If we are to understand that role, we must start by contemplating the world God created and the results His actions have. By doing this we can get an idea of where all this is heading and what our role is in that. We then act for the long term good of the whole not just as a selfish individual.