means A straight line that touches a curve at a single point without crossing it; figuratively, a sudden swerve off the main subject onto a loosely related one.

from From Latin tangentem, the present participle of tangere, 'to touch' — the same root that gives us tangible, tactile, and contact. Geometers borrowed it (via the phrase linea tangens, 'the touching line') for the line that grazes a curve at exactly one point. The conversational sense, 'going off on a tangent,' came later by metaphor: just as the line touches and departs, a speaker brushes the topic and shoots off in another direction.