Definition: A memory leak is a defect where software keeps hold of memory it no longer needs, so its memory use grows over time. Leaks often go unnoticed in short tests but can slow a system down or crash it after long running periods.
So what? Memory leaks are a common cause of performance problems that only appear in production or long test runs. Checking for them at code level, during development, is much cheaper than diagnosing them later.
Examples: A service that runs well after a restart but slows down over several days. A performance tester using a profiling tool during development to spot memory that is never released.