An acronym for triangulated irregular network, a TIN is a vector data structure that partitions geographic space into contiguous, non-overlapping triangles. http://support.esri.com/en/knowledgebase/GISDictionary/term/TIN
The vertices of each triangle are usually surface elevation sample data points. As such, a TIN is a common type of digital terrain model (DTM) and works best when the sample points are taken at intelligently located places on the terrain, that is, along ridges, valleys and other breaks in slope (and at peaks and pits) and when the triangle sides lie along said terrain lines. When the triangles are formed, they become simple planar facets of the terrain surface and then many DTM operations may be performed easily.
TINs need not be restricted to surface models; a TIN can be a simple alternative to a general polygonal vector structure. Each polygon, with a varying count of boundary segments, is replaced by component triangles, each with only 3 segments.