Pattern matching is needed in Rust to safely handle different shapes or types of data, especially enums that can hold different values. The program checks each pattern one by one until it finds a match. When a pattern matches, it can extract inner values for use. This prevents errors and makes code clear. If no pattern matches, Rust requires a default case or all patterns to be covered to avoid compile errors. The example shows matching a Shape enum with Circle, Rectangle, and Triangle variants. When the shape is Circle with radius 2.0, the match extracts the radius and prints it. This step-by-step matching and extraction is why pattern matching is essential in Rust programming.