The most common reason is that the JAVA version you have is old and that it has vulnerabilities, which may be being exploited.
Clear the JAVA cache and visit this site - it scans your system for out of date programs that have patches to close vulnerabilities, http://secunia.com/software_inspector/.
The Chest (quarantine) is a protected area and files in there can do no harm.
Finally, can I be assured that my computer will be secure if I quarantine? OR would it be better to delete them?
regard to security....no difference
but if the detection is a false positive and you need to restore......a big difference
in your case they are not system files so no problem deleting
These were in my C:\Documents and Settings*\Application Data\Sun\Java\Deployment\cache\6.0\12
and
C:\Documents and Settings*\Application Data\Sun\Java\Deployment\cache\6.0\48\13673cb0-3c6dbaa9
folders.
My java is up to date - is this just old file nonsense?
If you have the latest version of JAVA, which is JAVA 7 update 5, so I would guess and cache related to 6.0 would be old. I don’t have any reference to Application Data\Sun\Java\Deployment\cache\6.0\ in my JAVA only Application Data\Sun\Java\Deployment\cache, which is empty as I periodically clear the JAVA cache.