The claim that humans only use 10% of their brains has no basis in neuroscience and has been directly contradicted by every major imaging technique developed since — PET scans, fMRI, and EEG all show activity distributed across virtually the entire brain over the course of a normal day, with no substantial region sitting permanently dormant. The myth's actual origin is murky — it's sometimes attributed to a misreading of early 20th-century neurologist Karl Lashley's research on brain lesions, or to a misquote of psychologist William James's more modest claim that people don't reach their full potential, but there's no single clear source, and neuroscientists have been publicly debunking it since at least the 1970s without managing to fully kill it off.
What makes the myth durable despite being thoroughly false is that it maps onto a real and appealing idea — that people have significant untapped potential — even though the specific neurological claim attached to that idea is fabricated. Brain damage of almost any significant size, in almost any region, produces some measurable functional deficit, which is itself strong evidence against 90% of the brain being unnecessary spare capacity.
Beyerstein, a Simon Fraser University neuroscientist, spent years directly countering the myth in academic writing and public science communication, laying out the specific evidence against it: PET and fMRI studies consistently show activity distributed across virtually the entire brain over a normal day; brain-damage cases show that injury to almost any region, however small, produces some detectable functional deficit, which would be inexplicable if 90% of the brain served no function; and evolutionarily, an organ as metabolically expensive as the brain (using roughly 20% of the body's energy) would be an extraordinarily wasteful adaptation to carry around 90% unused.