Parallels Desktop 8 will run on OS X Mavericks (as the host), but Mavericks will not run (aka as a guest OS) on Parallels Desktop 8. This mainly impacts developer-types who want to run Mavericks as a test environment.
You can run Parallels Desktop 8 for Mac on OS X Mavericks and shouldn’t have issues, but you won’t have the benefit of all the new feature integration (of Mavericks into Windows programs), unless you upgrade to Parallels Desktop 9