Having a backup is necessary since we use our smartphone for almost all things and need to have a safe side to reduce the risk of losing important contacts, messages and valuable data. To do a backup sometimes we are required to reboot or to run recovery modes that consume lots of time. To have an easy backup without rebooting to recovery mode, the xda-developers.com made a really cool app called Online Nandroid Backup that can make live backup micro sd without doing any other thing on your phone. It supports easy renaming, deleting and compassing your backup.
To Install that app you need to root your OS with BUSYBOX and working CWM, TWRP or 4EXT based recovery installed. After installing the app from Google Play or alternatively download zip file from developer page and copy into Sd Card. Reboot to recovery mode and install zip file and reboot again.
After Installing the app you need to run app and start backup any time, also if you are playing a game. This takes averagely 5mins for 500mb.
For more assistance you can go to the developer forum here.