بُرہان   refers to irrefutable evidence, and in context of this verse, the irrefutable evidence being indicated is the Prophet صَلَّى الـلّٰـهُ عَلَيْهِ وَاٰلِهٖ وَسَلَّم himself. He was sent as an incontestable proof of how Allah is the only true God and Creator.^[1]

Muftī Aḥmad Yār Khan NaꜤīmī رَحْمَةُ الـلّٰـهِ عَلَيْه writes:

Miracles performed by the prophets عَـلَـيْهِمُ السَّلَام are proof of Allah’s being and attributes. Allah granted them varying miracles, such as the miraculous hand of Prophet Mūsā, the melodious voice of Prophet Dāwūd, and the profound beauty of Prophet Yūsuf.

In the same way, previous prophets were given one specific miracle. Some were given two. But when it came to his final and most beloved Prophet Muhammad صَلَّى الـلّٰـهُ عَلَيْهِ وَاٰلِهٖ وَسَلَّم, Allah made and sent him as a complete miracle from head to toe.^[2]

Allah then declared this complete miracle to be a clear and unquestionable proof, sent by Him to mankind.  

1. Prophetic miracles of his blessed body

Everything in this world is divided into two categories, کَثِیْف and لطیف.

*   کَثِیْف means tangible. These are things which can be physically grasped or used to cover something else. These make a shadow when light shines upon them. These could be doors, pens, walls, or anything else of substance.

*   لطیف means intangible. This refers to things that exist but cannot be touched or grasped. For example, wind, light and anything that does not cast a shadow.