Rashi states explicitly to Bereshit 21:8 that this was af the completion of the first 24 months of Yitzchok's life and as the Ikar Siftei Chachamim states, it coincided with Yitzchok no longer breast feeding from his mother, Sarah. Yitzchok began to consume wheat flour which is compared to Torah by Rabbi Elazar ben Azaryah like is found in Avot 3:17.
רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה אוֹמֵר, אִם אֵין תּוֹרָה, אֵין דֶּרֶךְ אֶרֶץ. אִם אֵין דֶּרֶךְ אֶרֶץ, אֵין תּוֹרָה. אִם אֵין חָכְמָה, אֵין יִרְאָה. אִם אֵין יִרְאָה, אֵין חָכְמָה. אִם אֵין בִּינָה, אֵין דַּעַת. אִם אֵין דַּעַת, אֵין בִּינָה. אִם אֵין קֶמַח, אֵין תּוֹרָה. אִם אֵין תּוֹרָה, אֵין קֶמַח.
So if you're looking for what celebration we actually do today that is associated with this, it would be the Upsherin, the first haircut given to a young Jewish boy after they enter their third year of life or as late as the completion of their 3rd birthday. At that time, the boy begins his formal Torah education and starts wearing tzitzit. See this Wikipedia page discussing the practice of Upsherin.
The difference in the two time ranges is to coincide with completing the 24 months like with Avraham, Sarah and Yitzchok, their son and the prohibition of Orlah, not benefitting from the fruit of Eretz Yisrael for the first 3 years.
Upsherin is practiced by many different Chassidic branches, Kabbalists following the teachings of the Ari z"l, and as noted in נטעי גבריאל - תגלחת הילדים הולכתם לחדר וסעודת החומש, Chapter 2, page 35, footnote 2, this is also the practice of some of the Jews of Yemen.