This question raised the point that it is hard to distinguish the term 'illah (criterion, Arabic: عله) from hikmah (benefit, Arabic: حكمه) when it comes to ahkām al-fiqh (rulings of jurisprudence, Arabic: أحكام الفقه) which may cause misunderstandings of the rulings and their applications.
Question: What are the characteristics of 'illah and what is its governance? The governance of 'illah is a bonus part.
By governance of 'illah, I am referring to the principles of jurisprudence that provide the applicability of the ruling (the ruling is tied to the criterion's presence and absence, Arabic: الحكم يدور مع علته وجودا وعدما), the interpretation of its wording (what counts is the general meaning of the words, not the specific reason for revelation, Arabic: العبرة بعموم اللفظ لا بخصوص السبب), and accepted deduction methodologies (setting criteria based on perceived benefit or through qiyās for permissibility, Arabic: التعليل بالحكمه او بالقياس فى الرخص), as examples. An answer using a single school of jurisprudence is sufficient.