Safe Mode
Safe mode is a feature of Cydia Substrate that prevents your device from entering a permanent crash cycle by giving you a chance to uninstall malfunctioning extensions without a complete device restore.
Below are instructions for help on how to get your device back in working order. Only continue on to the next step if the previous one was not able to solve your problem.
1: Just Restart
If this is the first time you have entered safe mode, just tap the status bar at the top of the screen and click Restart to restart your SpringBoard. If this was an isolated issue, this should be enough to get you going again.
If you've already tried the above, and you're back in Safe Mode, read on.
2: Remove Recently Installed Extensions
If you recently installed a new tweak or extension in Cydia, try uninstalling that tweak. Open up Cydia, go to Installed, tap Recent, find the tweak and tap it, tap Modify in the top-right corner, and tap Remove to uninstall it.
Especially try uninstalling any extensions that may not be compatible with your device's iOS version (often the description page for an extension mentions which iOS versions it is compatible with). Also make sure you're using extensions from trusted repositories such as BigBoss, ModMyi, and ZodTTD & MacCiti.
If you haven't recently installed an extension, or uninstalling it didn't help, read on.
3: Determine Cause
If you are still stuck in Safe Mode, you can try to diagnose the problem using an app called Crash Reporter. Open that up, select SpringBoard, and choose the top crash. Crash Reporter will try to provide an automated guess as to what extension caused the crash. If it finds something, try removing that package in Cydia. (Be careful about uninstalling packages you don't recognize, in case they're packages that Cydia needs.)
You should also send the developer of the extension the crash log found by Crash Reporter, so they can fix the issue in an update to their package.
If Crash Reporter can't find what causes the crash, or removing the tweak it finds doesn't help, read on.
4: Ask for Help
If you still can't get your device back in working order, your next best bet is to ask for help. You can ask a forum such as JailbreakQA or /r/jailbreak; make sure to include a list of your installed tweaks so that other people can help make guesses about the problem.
If nobody is able to provide help to get your device working again, read on.
5: Restore
If all else fails, you can always restore with iTunes, which will also automatically update your device to the latest iOS version. Before you try this, you should check Cydia's help pages to find out whether the latest iOS version can be jailbroken. Don't upgrade to an iOS version past what is able to be jailbroken: you likely cannot come back.