Hi Darryl,
Jing records what is on your screen, but possibly not DVDs. If you are using the DVD Player built into Mac OS, you will likely find that Jing will only record a checkerboard and not your video. This is because of DRM built into Mac OS.
Other users have reported success recording DVDs with Jing when they use third-party playback software like VLC.
You will get the best results by ripping the DVD using software like Handbrake and then editing the resulting video (using software like Camtasia Mac or Adobe Premier) to the section(s) you want and then save it as an mp4.
-Glenn
