Overall purpose of all rituals is Tazkiya (cleansing) of either body, soul or both. Specific wisdom for each ritual is explained by God in Quran at different places:
Salat:
* It’s purpose is the remembrance of God (20:14);
* To seek support of God (2:153);
* It increases wisdom and understanding (11:87);
* If done correctly, it prohibits evil & vice (29:45);
Fasting:
* Obligatory Fasts: To increase God-consciousness (2:182);
* Expiation Fasts: Other than the ‘annual’ fasting in Ramadhan, there are different fasts mentioned in the Qur’an as an expiation for certain sins. (5:89, 2:196, 58:2-4, 4:92).
Charity:
* Repentance and purification (9:103-104).
Pilgrimage:
* For attendees to witness benefits for themselves (22:28-29). What are the benefits? Hajj gathering opens the door to opportunities of trade, information exchange, cultural exchange, networking, etc. This idea of the meeting and mixing of people/races can be clearly seen in verse 49:13;
* The second objective of Pilgrimage comes from the word “Hajj/Pilgrimage” itself which means: “to debate,” thus, during the days of Pilgrimage, the people are able to share and discuss with each other their understanding of the system of God, of the laws, government, and the teachings that He has decreed to us through the prophets (both physical and spiritual);
* The third objective of Pilgrimage comes from the animal sacrifice, which involves feeding the poor, and feasting on God’s bounty (22:28-29).
Reference : The Natural Republic (https://www.free-minds.org/sites/default/files/TNR.pdf)