Toughness in a polymer refers to its ability to absorb energy and deform plastically without fracturing. It is quantitatively represented as the area under the stress-strain curve, which gives the total energy absorbed by the polymer before failure. This includes both elastic and plastic deformations. The Izod and Charpy impact tests measure impact resistance but are not direct indicators of toughness. Depth of indentation is related to hardness, not toughness.
Thus, the correct answer is:
\[
\boxed{\text{(C) Area under the stress-strain curve.}}
\]