Ductility is a property of materials that indicates their capacity to undergo significant plastic deformation before fracture. This means that ductile materials can be stretched into a wire or deformed in other manners, without breaking. In essence, this property allows the material to change shape and absorb energy without fracturing.

Let's analyze the options to identify why "Undergo plastic deformation before fracture" is the correct answer:

1. Resist surface indentation: This property is related to hardness, not ductility. Hardness measures a material's resistance to localized plastic deformation, such as indentation.
2. Undergo plastic deformation before fracture: This is the definition of ductility. Ductility allows a material to deform plastically before it fractures, which is a key characteristic of metals like gold, silver, and aluminum.
3. Return to its original shape after unloading: This property is known as elasticity. Elastic materials return to their original shape after the deforming load is removed.
4. Conduct heat efficiently: This describes thermal conductivity, which is a measure of how well a material can conduct heat, not related to ductility.

Thus, the correct answer is that the ductility of a material refers to its ability to "undergo plastic deformation before fracture."

In summary, ductility is an essential property for applications requiring materials that can sustain deformation under tensile stress, such as manufacturing wires, components that require molding, and structural elements that must absorb significant energy before breaking.