A triangulation T of Rn+1 is a subdivision of Rn+1 into (n+1)-simplices such that: 1. any two simplices in T intersect in a common face or not at all; 2. any bounded set[?] in Rn+1 intersects only finitely many[?] simplices in T.
A Delaunay triangulation is the dual of a Voronoi tesselation.
[As it stands, this article is an excrutiatingly short stub.]
Some useful links:
http://www.cs.cornell.edu/Info/People/chew/Delaunay
http://goanna.cs.rmit.edu.au/~gl/research/comp_geom/delaunay/delaunay
http://astronomy.swin.edu.au/~pbourke/terrain/triangulate
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