A capillary was the smallest type of blood vessel and a part of the circulatory system in humanoid lifeforms.
In 2365, during Captain Jean-Luc Picard's cardiac implant replacement surgery, the surgeon noted that there had been some capillary reaction and the surgical team needed to proceed carefully. (TNG: "Samaritan Snare")
In 2370, Reginald Barclay anxiously informed Doctor Beverly Crusher that he thought his capillaries were shrinking. (TNG: "Genesis")
In 2372, the capillaries in Jake Sisko's cerebral cortex dilated 20 percent, due to Onaya's stimulation of his brain. (DS9: "The Muse")
In 2374, Seven of Nine noticed that the capillaries in "Tom Paris"'s eyes were swollen (actually an identity thief), leading her to believe that he was intoxicated. (VOY: "Vis à Vis")
When Species 8472 imitated Humans and recreated Starfleet Command, their simulations were indiscernable from the real thing. The Doctor scanned the David Gentry-impersonator, finding no difference down to the capillaries. (VOY: "In the Flesh")