The ArrayIndexOutOfBoundsException is a runtime exception in Java that occurs when an array is accessed with an illegal index. The index is either negative or greater than or equal to the size of the array. Let’s put that in simpler terms with an analogy. Imagine you have a row of five boxes lined up in front of you. Each box has a number on it. If you want to put a toy in one of these boxes, you have to say which box number you're putting it in. For example, "Put this toy in box number 2.".

When you run a Java program, the Java Virtual Machine (JVM) needs to load various classes to execute the program. The java.lang.ClassNotFoundException occurs when the JVM tries to load a particular class but doesn’t find it in the classpath. One of the most common reasons for the ClassNotFoundException is missing third-party libraries. Double-checking that all necessary dependencies are included in the classpath and that the classpath is correctly configured can prevent this exception.

Java.lang exceptions are some of the most commonly encountered exceptions in Java programming. As one of the foundational packages in the Java Standard Library, you don't even explicitly import java.lang in your code; it’s automatically imported into every Java program. Thanks to java.lang you get essential classes such as String, Math, and System, among others. You also get a variety of base classes for handling exceptions and errors.