Real programs face conditions they cannot control: a file is missing, a network drops, user input is malformed, a calculation divides by zero. Exception handling is Java's structured mechanism for dealing with these abnormal situations without letting them silently corrupt data or crash the program in confusing ways. Rather than checking a return code after every operation, Java lets code that detects a problem throw an exception, transferring control to a handler that catches it.
Java distinguishes checked exceptions, which the compiler forces you to handle or declare, from unchecked exceptions (runtime exceptions and errors), which it does not. It also provides try-catch-finally for handling, try-with-resources for automatic cleanup, and the ability to define your own exception types. Understanding all of this matters because how you handle failure determines whether a system degrades gracefully or falls over, and whether the next developer can diagnose what went wrong.
Exception handling done well makes failure explicit, recoverable where possible, and diagnosable where not; done poorly, swallowed exceptions and vague error messages, it produces systems that fail mysteriously and resist debugging. Mastering the model is what separates code that merely works in the happy path from code that survives the real world.