Step 1: Read the definition given in the question.
The question defines: the obligation of a subordinate to properly perform the assigned duty. We need to identify what this is called in management.
Step 2: Recall the three elements of delegation.
Delegation involves three interconnected elements: Authority, Responsibility, and Accountability. Each has a precise meaning, and it is important not to confuse them.
Step 3: Understand Authority.
Authority is the right or power vested in a manager to give orders, make decisions, and direct subordinates. It flows downward from superior to subordinate.
Step 4: Understand Responsibility.
Responsibility is the obligation that arises from a subordinate's duty to perform the task assigned to them. When a superior assigns work to a subordinate, the subordinate becomes responsible (obligated) to complete that work properly. This exactly matches the definition given in the question.
Step 5: Understand Accountability.
Accountability is being answerable for the final results or outcomes of the work. It is one step beyond responsibility: even if you delegate work to someone below you, you remain accountable to those above you for the results.
Step 6: Match and conclude.
The term for the obligation to perform an assigned duty is Responsibility, which corresponds to option (C).
\[ \boxed{ \text{(C) Responsibility} } \]