The importance of unit testing in software development cannot be overstated, as it ensures that individual components of the application code behave as expected and catch defects early on. Writing unit tests for Java code can be achieved using various frameworks such as JUnit 5, which provides a comprehensive framework for writing and running unit tests. By installing JUnit 5 and adding it to the Maven project, developers can create test classes that cover different scenarios of their application's code, including edge cases like SQL injection vulnerabilities. The process involves importing required packages, defining test methods using the `@Test` annotation, and verifying the expected output or behavior of the code under testing. This practice adds a layer of defense against breaking core functionality and releasing unstable changes into production applications, making it an essential part of any developer's toolkit.