All Exceptions *except* RuntimeException and its descendants must be
declared by any method that can possibly throw them or allow them to
propagate.  These are the "checked exceptions".  RuntimeException and
its subclasses are "unchecked exceptions"; they do not need to be
declared by methods that throw them or allow them to propagate.  Those
are the basic differences.

(Error and its subclasses are not technically exceptions, but they are
another type of unchecked Throwable.)

Whether a particular application-specific exception class should be
checked or unchecked, and in general whether to use checked or unchecked
exceptions are entirely different and more subjective questions.