Bug statistics are a way to learn more about type of bugs, may be indirectly to learn more about how developers and tester are performing, to learn more about the product etc.
Bug statistics help us determine the proper amount of testing for a system.
Bug statistics from one project may help in other (similar) projects in future.
Bug statistics may also help you improve your testing or reporting.
Bug statistics help us determine which areas of the system generate the most problems.
Bug statistics are different for different products/projects/circumstances etc.
Some of the examples of bug statistics are:
[may be some are overlapping]
Total bugs opened.
Bugs opened in last 7 days.
Bugs closed in last 7 days.
Bugs opened in the last 30 days.
Bugs reported today.
Number of bugs per developer.
Number of times a bug is reopened.
Number of bugs fixed in a build.
Number of bugs fixed in a release.
Number of bugs per module.
Total bugs verified.
Total bugs confirmed.
Defects by Status (open, in progress, rejected, deferred, resolved).
Defects by testing phase (unit testing, system testing etc).
Defects by tester.
Defects by severity.
Defects by business priority.
Defects by root cause [functional specification, System OS etc].
Defects by injection phase [requirements, design..].
Bugs assigned to each tester/developer.
and so on...