The physical characteristic that defines the mass of a substance contained within a specific volume is known as density.

Density is expressed mathematically as:
Density = Mass / Volume

- This means that density measures how much mass is packed into a given volume of a substance.
- It is a fundamental property used to identify materials and understand their behavior under different conditions.

To clarify the other options:
- Specific Gravity is a ratio comparing the density of a substance to the density of a reference substance (usually water), and it is a dimensionless quantity.
- Viscosity describes a fluid’s resistance to flow, not related to mass or volume.
- Surface Tension refers to the elastic tendency of a fluid surface, which allows it to resist external force, unrelated to mass per volume.

Therefore, the correct answer is Density because it directly defines the relationship between mass and volume.

Reference: Physics for Health Sciences, Volume 1, Chapter 3: Properties of Matter, Page 45