A layman was a person who possessed no accreditations in or advanced knowledge about a given field.
While cross-examining Doctor Julian Bashir in 2369, Ilon Tandro referred to himself as a layman in relation to the field of medicine. (DS9: "Dax")
In 2371, pleased by Kes' curiosity about anatomy and physiology, The Doctor gave her several medical texts to study, cautioning her that they weren't written for laymen. (VOY: "Eye of the Needle")
Later that year, he likewise cautioned Tuvok when the Vulcan asked for a copy of his neurological analysis of Tom Paris calling the report "virtually indecipherable" to the layman. (VOY: "Ex Post Facto")