When DDMS attaches, it uses the same connection as a debugger. When it disconnects, you get that message. Had an actual debugger been attached, the object registry would have more than one entry in it.
Try this: with the DDMS view active in Eclipse, disconnect USB, then reconnect it. If you scroll back in logcat you should see that, when the USB connection dropped, a "debugger has detached" message was emitted by every debuggable app that was running.
Apps are only debuggable if they have the android:debuggable
flag set in their manifest, or you're on a developer ("userdebug") device (which has the system property ro.debuggable
set to 1). If you're on a production device, you'll generally only see the "detached" message for apps you're developing that happen to be running.
You can safely ignore the message.