Many problems in computational geometry require polygons to be broken into triangles. This process is called triangulation. See the figures below (on the left: a polygon; on the right: a triangulated polygon).
The Process
There are many ways to divide a polygon into triangles. One method involves removing ears from the polygon. An ear is a triangle formed by three consecutive points of a polygon. Note that three consecutive points of a polygon do not necessarily form an ear - if the line segment between the first and third point intersect with the border of the polygon, or if this line segment lies outside the polygon completely, the three consecutive points do not form an ear. See the figures below (on the left: three consecutive points forming an ear; on the right: three consecutives points that do not form an ear).
Triangulation can be performed by finding an ear of a polygon, removing the ear, and then repeating this process until the polygon is reduced to a single triangle. The difficult part of this process is finding ears quickly. The simple, brute-force method of finding an ear of a polygon is to first test the first, second and third points of the polygon to see if they form an ear; if they don't, then test the second, third and fourth points, etc. until an ear is found. A faster (and more complicated) method involves dividing a polygon into progressively smaller pieces, until an ear is found or until the polygon is reduced to a single triangle, whichever comes first. A technical paper on how this is done can be found here.