A splinter was a fragment of a substance, usually wood, that became subcutaneously lodged in a person's body.
In 2268, when attempting to express the immense difficulty of performing surgery to reunite his brain with his body, Spock said that he would trust Doctor McCoy to remove a splinter or lance a boil but not to attempt such a surgical procedure. (TOS: "Spock's Brain")
In 2372, while showing some Drayans around USS Voyager's sickbay, The Doctor assured First Prelate Alcia that they could perform "a wide variety of treatments here, from removing a splinter to re-sequencing the base pairs in a strand of DNA". (VOY: "Innocence")