All right, let's begin explaining what exceptions are. Just as in other programming languages, this applies to Java as well: exceptions are those errors that occur during runtime. These aren't real errors, because they are exceptions. One might call them exceptional events that can and should be handled to continue program execution. So there's "something" one has to do about them.

One of the most remarkable examples of exceptional cases and conditions is when, during program execution, the time comes for a division by zero. This cannot be done and, therefore, Java throws an exception, specifically the ArithmeticException. From the Java programmer's point of view, exceptions are objects. Throwing exceptions is akin to throwing objects. But here's the drill: not every object can be thrown.

In order to fully understand throwable exceptions, some parts of the entire class hierarchy should be presented. There is one main class called Throwable. This class has two sub-classes: Exception and Error. An exception object must be descended from a class that is Throwable, meaning it must be an object instance of either an Exception sub-class or Error sub-class. These can both be found in the java.lang package.

Exception handling is the technique of catching the exceptions that might be thrown some time in the future during runtime. Java offers robust exception handling solutions with the try-catch-finally construct. On other hand, you can work with already-declared exceptions, such as the ArithmeticException, NullPointerException, and others. Other classes extend the Exception class-e.g., the IOException subclass from java.io. 

Furthermore, we should also note that exceptions are of two kinds: unchecked and checked. Unchecked exceptions are technically RuntimeExceptions (or its subclasses). These don't need to be declared in your throws clauses, and catching them is optional, but many don't bother-they occur without the knowledge of programmers, who may not even know that those are "catchable." Most of the time, these are logic programming errors such as NullPointerException or ArrayIndexOutOfBounds.

Meanwhile, checked exceptions technically force the programmer to handle and manage them, meaning catch and cover them individually. These are derived from the Exceptions class and its subclasses, excluding the RuntimeExceptions as we discussed in the paragraph above (those are unchecked!). Checked exceptions require exception handling because they might cause program termination.

Now that we've learned the basic theory, let's fire up our IDE, and start coding!