The Galaxy Note 2 Safe Mode works much like that with Windows-based computers. It only loads the stock apps or the basic programs that the device needs in booting up successfully.
Entering the Galaxy Note 2 Safe Mode is a basic troubleshooting method that will enable you to detect if one or more apps that you have installed are causing the errors that you are experiencing with your Android phone.
The reason why it's booting up in safe mode sometimes is because you're accidentally executing it's button combination when you turn on your phone! Below ate the instructions on how you enable or disable this mode when turning your phone on for your future reference.
''Enabling the Samsung Galaxy Note 2 Safe mode:
''
1. Turn off the Galaxy Note 2 by pressing the Power button (positioned in the right edge of the device). Tap Power Off from the choices that will appear followed by OK.
2. Once the device successfully shuts down, press the Power button again, but this time, keep your finger pressed on it together with the Volume Down button.
3. Let go of the Power button when you see the Samsung Galaxy Note II logo but do not let go of the Volume Down key yet.
4. After that, you will see a status message telling you that your Galaxy Note 2 is now in Safe Mode. Let go of the Volume Down key and tap the OK button.
'''Disabling the Galaxy Note 2 Safe Mode'''
To exit the Galaxy Note 2 Safe Mode, all you have to do is turn off your phone normally using step 1 above. Then, power it on using the usual way.
Hope this helps you understand what's going on & why! If this helped you out, feel free to express this by "accepting" my solution as your chosen answer!
Cheers