The panpsychist argument usually starts from a version of the hard problem: physical science describes structure and function, how parts of a system relate and behave, but never touches the intrinsic, felt quality of experience, and no amount of added structural detail seems able to close that gap by itself. Rather than accepting an unexplained emergence of experience once matter becomes complex enough, as standard materialism does, panpsychists propose that some primitive form of experience is there in matter from the start, however faint, and that complex consciousness in brains is a highly organized combination of vastly simpler experiential elements already present in their basic physical constituents.
Alfred North Whitehead built the most systematic version of this in Process and Reality, arguing that the ultimate units of reality are not enduring bits of matter at all but momentary events of experience, each one prehending, taking account of, the events that preceded it, with what we call material objects being stable patterns of these experiential events rather than the basic furniture of the world. The position's hardest problem in turn is the so-called combination problem: explaining how many simple, separate micro-experiences, in atoms or particles, could combine into the single, unified experience of a person, rather than remaining a mere crowd of tiny separate perspectives.