It is the normal translation of the Greek term nous.
In Islam, the term ‘aql was heavily elucidated by early Shī‘ah thinkers; it came to replace and expand the pre-Islamic concept of ḥilm (Arabic: حلم) "serene justice and self-control, dignity" in opposition to the negative notions of ignorance (jahl) and stupidity (safah).
The "possessor of ‘aql", or al-‘āqīl (plural al-‘uqqāl) realises a deep connection with God.
Jaʿfar aṣ-Ṣādiq (d. 765, notably an Imām) described this connection as a realisation that God loves some, that God is truth and that only ‘ilm "sacred knowledge" and its development can help humanity fulfil its potential.
His son, Imām Mūsà al-Kāżim (d. 799), expanded this exegesis by defining ‘aql as the "faculty for apprehending the divine, a faculty of metaphysical perception, a light in the heart, through which one can discern and recognize signs from God."
He further noted that where the A'immah (Imāms) are the ḥujjatu ż-żāhira "External proof [of God]", ‘aql is the ḥujjatu l-Bāṭina "Secret proof".
While in early Islam, ‘aql was opposed to jahl "ignorance", the expansion of the concept meant it was now opposed to safah "[deliberate] stupidity" and junūn "lack of sense, indulgence".
Under the influence of Mu‘tazilī thought, ‘aql came to mean "dialectical reasoning".
Along with the Universal Soul (al-Nafs al-Kull), they explained that it presides over the spiritual world.
These archangels are paralleled in the physical world by the enunciators of divine revelation (nāṭiqs) and the foundation of its esoteric interpretation (asās).
Shī‘ī Legal Implementation
In Shī‘ī jurisprudence, ‘aql is the process of using intellect or logic to deduce law.
Legal scholars in both Sunni and Shī‘ī Islamic traditions share Quranic interpretation, the Sunnah, and Ijma‘ "consensus" as sources of Islamic law and judicial decisions (ḥukm).
Among Twelvers, Akhbārīs (associated with exotericism and traditionalism and theological schools in Qom) and Usulis (associated with esotericism and rationalism and theological schools in Baghdad) were contending subschools: the former reject ijtihād outright; the latter advocate ijtihad and have been predominant for the last 300 years.
In Shī‘ī Islam, "the gates of ijtihād" were never closed and with the use of ‘aql, Shī‘ī mujtahids "practitioner of ijtihād" and faqīhs "legal specialists" are able to respond as issues arise that were not explicitly dealt with in the Qur'an or Sunnah.
Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/'Aql.