Every Yom Tov, says the gemara in Pesachim (68b), is "Chetzyoi LaShem V'Chetyoi Lachem" (half for Hashem and half for you). Of course it is all for Hashem but our celebration has two parts. One part in pure spiritual devotion like davening and learning and the other part is more earthly through eating (albeit with the goal of Kiddush Hashem).
What about Yom Kippur, where is the Chetzyoi Lachem as we are wrapped in talis and fast all day? The Vilna Gaon answers that the Lachem part of Yom Kippur is Purim. Purim is the completion of Yom Kippur. It is the physical half. Moreover say Chazal, Purim is the holier half as Yom Kippur is only Yom "K"Purim a day whose kedusha only approaches the incredible kedusha of Purim.
Rav Shimshon Pincus says that some Meforshim explain the connection between the two with the Chazal that says "Kol HaPoshet Yad Nosnim Lo" (whoever opens his hand is given to). Just like on Purim where we are obligated to give tzedaka to whoever stretches out his hand, so to on Yom Kippur Hashem gives us whatever we ask for. Purim is a day where Hashem also gives whatever we ask and is more effective than Yom Kippur when we need to fast and daven to get it. Purim we can be in a state of obliviousness "Ad D'Lo Yadah" and still get what we need.
Rav Shimshon Pincus himself offers that there are three days of celebration of Matan Torah during the year. Shavuos where we celebrate the first Luchos with the hearing of them on Har Sinai, Yom Kippur when we received the second luchos, and Purim when we finally accepted the Torah by our own volition without being forced. This was the most joyous kabalas HaTorah that came from a physical revelation that the torah is in our best earthy and heavenly interest. That is why on this Kabalas HaTorah we celebrate in a most earthly way.