Rabbi Rabbi Shaya Karlinsky presents some thoughts from the Maharal to explain. Teshuvah means return. Via proper teshuvah we return to Hashem. The Maharal explains that these three activities parallel the Torah, Avodah, and Gemillas Chasadim upon which the world stands (as listed in Pirkei Avos), which in turn parallel the intellectual, emotional, and physical domains of existence.
In Nesiv HaTeshuva, Ch. 5, the Maharal writes:
A principle and a foundation of Teshuva is that a person should be embarrassed over the sin he has done, and because of his embarrassment he is received in teshuvah. (Berachot 12b): “Rav Chinina Saba says in the name of Rav: ‘Anyone who commits a sin and is embarrassed, has all his sins forgiven…’ “
This is the intellectual component of the formula, a recognition that we have not lived up to our potential. Through confession to Hashem, we connect to Him in humility.
Now that we have an intellectual recognition, we turn to prayer. We give our hearts over to Hashem in humility. In Nesiv Ha’Avodah chapter 1, the Maharal writes:
When man prays before G-d, declaring his need and dependence, he shows that he belongs to G-d (the way a slave belongs to an owner because of his dependence). This is why prayer is the essence of service, as it demonstrates man’s complete dependence on and subjugation to G-d.
Lastly, we turn to tzedukah. Through the giving of tzedukah, we give our physical selves. We show our recognition that our possessions are gifts from above to be used in divine service. In Nesiv Hatzedaka, chapter 1, the Maharal writes:
Whenever one bestows charity on others, G-d assists him by providing more money that enables him to continue bestowing charity on others. This is because one who bestows on others is compared to a flowing spring whose waters flow great distances. G-d, who is the source of all bounty bestows resources upon this person in order that he should be able to bestow and share these resources.
Tzeduka connects us to the source of bracha by making us a conduit to the giving of bracha to others.