DTM is an acronym for digital terrain model -- a data structure providing values for elevation (or some other geographical variable) as an empirical function of horizontal position.
The simplest DTM data structure is a set of unlinked, irregular sample points, each having an X-Y-Z triplet (though some may argue that it doesn't qualify as being a DTM).
A common structure is the TIN, an extension of the above simple one where neighboring points are linked together to form a network of non-overlapping triangles. (TIN = triangular irregular network.)
Another common structure is a gridded DTM. This is a raster structure (a 2D array) where the pixel values are the surface elevations. While this type of DTM is sometimes known as a digital elevation model (DEM), DTM and DEM are often synonyms (typically outside the USA).
A controversial DTM structure is the (digitized) contour map: a set of vector lines, each of a certain elevation. The criticism is that these represent cartographic artifacts rather than the actual terrain surface. In its defence, the contour map may be the only source of data available.
Along with a DTM (or part of it, if it is programmed as an object/class) are various operations that are usful in cartography and GIS: spatial interpolation, contouring, 3D viewing, volume estimation, and slope analysis.