The Brain is an object pertaining to the first test of the Key to the Abyss, also referred to as level of Dominion. The challenge of this particular trial consists in acquiring sixteen brains from inside the gloomy and misleading Brain Maze and inserting them into a peculiar apparatus, in order to spawn a major demon, Vine, whose demise will yield us the Power of Dominion scroll and allow us to proceed unto the next test of Sheol, the Halls of Doppelgangis.
On a humorous side note, the name given to the Brain texture (as extracted from the INTRPLAY/ROTH/M/ADEMO.DAS file) is called "BRAIN1.Keith's brain.bmp", referring to one of the game's developers, Keith Dando.
Is there any significance to the number of the brains, Sixteen? In the Rider Waite tarot deck, the Tower is the 16th trump or Major Arcana card, but I doubt this has anything to do with it. Maybe the developers were just going for an excessive large amount to symbolize the irrationality of the trials and puzzles in Sheol, to visualize the deterioration of the mind, the fall into insanity.