An indeterminate form occurs in calculus when evaluating limits that do not lead to a clear or defined value. Common examples include expressions like 0/0, ∞/∞, and ∞ - ∞. These forms require further analysis, often using techniques such as L'Hôpital's Rule or algebraic manipulation, to determine the actual limit. Indeterminate forms arise in various mathematical contexts, particularly when dealing with limits of functions as they approach specific points. Understanding these forms is crucial for solving problems in calculus, as they indicate situations where standard evaluation methods fail to provide a definitive answer.