Respringing is the term for restarting the device's SpringBoard. The process takes about 10 seconds and, by default, returns you to the Lock Screen. Mobile Substrate does this to exit Safe Mode if the SpringBoard crashes. Many SpringBoard extensions may respring for other reasons. For instance, WinterBoard resprings when you change theme settings and vBackground will respring when you change the video. This is not the same as a reboot.
A "hard" respring involves issuing a "killall SpringBoard" command as either root or mobile user, which terminates the SpringBoard. The SpringBoard will be relaunched immediately afterward, but takes a few seconds to fully load while a spinning wheel is displayed.
SpringBoard's daemon, referenced at /System/Library/LaunchDaemons/com.apple.SpringBoard.plist will quickly reload the GUI. (While this is accomplished, the previously mentioned spinner will appear stationary.)
The lockscreen will then appear on screen, unless the ~/Library/Preferences/com.apple.springboard.plist file contains
In which case the first page of applications will immediately appear.
A "soft" respring (as employed by SBSettings or Rename II, for example) uses a Darwin notification and the
preference to emulate the "on language change" soft restart, which returns to the Home Screen, not the Lock Screen, by default.