[linear referencing]
In linear referencing, a measure value that is added to a line feature. M-values are used to measure the distance along a line feature from a vertex (a known location) to an event.
[ESRI software]
Vertex attributes that are stored with x,y point coordinates in ESRI's Geometry Engine. Every type of geometry (point, polyline, polygon, and so on) can have attributes for every vertex.