It means that the bisector of an angle A in an angle divides the third side CB into BD and CD, then AB/AC=DB/DC.

The evidence is simple. Analyze the areas of two triangles ABD and ACD.

Consider that A is the vertex, BD(CD) is the bottom, and the heights of the two triangles are equal (both are the distance from A to BC), so the area ratio is equal to the ratio of the bottom, that is, BD/CD;

Consider whether the heights of two triangles are equal with D as the vertex and AB(AC) as the base (because the distances from the point on the angle bisector are equal), and the area ratio is equal to the ratio of the base, that is, AB/AC;

Therefore: BD/CD=AB/AC.