Consistency of cohesive soils refers to the ability of the soil to resist deformation and maintain its form under applied stresses. It is an important parameter in geotechnical engineering as it affects the shear strength and compressibility of the soil.

Factors affecting consistency:
- Moisture content: As the moisture content of the soil increases, the consistency of the soil changes from a solid to a plastic, and eventually to a liquid state.
- Density: The density of the soil affects its consistency, as denser soils are generally more cohesive and have higher shear strength.
- Type of cohesive material: Different types of cohesive materials have different consistency characteristics. For example, clay soils typically have higher consistency than silt soils.

Importance of consistency:
- Shear strength: Consistency is directly related to shear strength, as soils with higher consistency have higher shear strength.
- Compressibility: Consistency affects the compressibility of the soil, as more consistent soils are generally less compressible.
- Engineering properties: Consistency is an important parameter in determining the engineering properties of cohesive soils, such as their bearing capacity, settlement characteristics, and stability.

Therefore, the correct option is C) shear strength, as consistency is an indicator of the soil's ability to resist deformation and maintain its form under applied stresses, which is directly related to its shear strength.