Boltzmann brains are a hypothesis that given fluctuations of entropy levels within our universe, it is far more likely that simple conscious “brains” would form out of the continuing chaos that is thermodynamic / quantum field permeating our universe, than all the billions and billions of galaxies etc that we do see.
It’s known as the Boltzmann Brain Problem/Paradox after Boltzmann who himself suggested that a system with a high entropy would occasionally, through random interaction, slip into a low entropy state. Mostly these dips wouldn’t result in much because they’d normalise fairly quickly. But if a system were running indefinitely or even eternally, then the probability is likely to occur at some point that enough of a low level is achieved to explain such complexity as our universe as we know it “beginning”. An answer to the question of why our universe had such a low entropy level in the beginning.
As an aside; if we’re going to use the current entropy level as a benchmark then any past point is going to be lower entropy. That’s how time works.
The reason the problem isn’t a problem is because using observers as a benchmark for what the universe pops into existence through fluctuation is not what we observe. The most we observe are particles. We observe energy. We observe the effects of Dark Matter and Dark Energy. We don’t observe brains without evolution.
We’re here because of a long process we understand through mainly classical physics and chemistry etc. The fluctuation of entropy (i.e. the arrangement of matter in a system) is only needed to explain the proto-universe, the reason for the plasma and energy fields which coalesced into matter which then interacted to form more complex structures and so on until we reach galaxies and planets and physicists and William Lane Craig etc.
We observe fluctuation entirely within reason for the average drop of entropy with particle physics and quantum field theory.
The brains aren’t probable because there are mechanisms build on systems which require prerequisite chemical interactions to achieve.