The claim
Panpsychism says that experience does not appear out of nothing when matter gets organised into a brain. It is there from the start, as a basic feature of the physical world, in some minimal form. Brains are special because they combine and concentrate it.
Put that way it sounds mystical. The modern argument for it is dry and comes from the hard problem.
Why philosophers take it seriously
Physics describes what matter does: masses, charges and how they interact. It says nothing about what matter is intrinsically. This observation goes back to Bertrand Russell and Arthur Eddington in the 1920s.
We know one case where we have access to the intrinsic nature of some matter: our own brains, from the inside, as experience. Russellian monism proposes the simplest fit: the intrinsic nature that physics leaves blank is experiential, or proto-experiential, everywhere. Then consciousness has a place in nature without adding anything to the equations.
David Chalmers, Philip Goff (Galileo's Error, 2019) and Galen Strawson have developed versions of this argument. It explains why panpsychism moved from fringe to a respectable position in philosophy of mind over the last twenty years.
The problems
Combination. If an electron has a flicker of experience, how do the flickers of a hundred billion neurons' worth of particles become one unified point of view? Adding small experiences does not obviously produce a single larger subject. This is the problem panpsychists themselves consider the hardest.
Testability. Panpsychism, as usually stated, predicts no observation that a physicalist would not also predict. A stone behaves the same whether or not it has a trace of experience. A hypothesis that forbids nothing is hard to count as science.
Where the line goes. If everything has experience, the interesting question becomes which systems have unified experience, and that needs a structural criterion, which brings us back to theories like IIT.
Relatives: IIT and cosmopsychism
Integrated information theory is sometimes called panpsychist because it attributes some consciousness to any system with integrated information. It is more selective than classic panpsychism: a pile of sand has almost none, however many particles it contains.
Cosmopsychism flips the direction: the universe is the basic subject, and individual minds are fragments of it. It avoids the combination problem and inherits a mirror-image one: how does one cosmic subject split into many private viewpoints?
Is the universe conscious?
There is no evidence that it is, and no agreed way to measure it. What can be measured is structure: how information is integrated and exchanged at different scales. The brain and the cosmic web share some network statistics, and physical law can be written in informational terms. Those facts make the question of consciousness at cosmic scale thinkable. They do not answer it.
The research programme on this site stays on the measurable side. It asks whether the universe processes information like a network and builds that idea as a working computational substrate with falsifiers stated in advance. Whether such processing is accompanied by experience is left open until someone finds a way to measure it.
Bottom line
Panpsychism is a serious philosophical answer to the hard problem with two unsolved difficulties: combination and testability. A version worth adopting in science would have to name a structural quantity and predict where rich experience appears and where it does not. IIT is the closest attempt so far.