How To Backup Your Android Device Without Rooting Or Unlocking

You don't need to root your device to back it up, most android smartphone comes with an inbuilt way to restore or backup your android phone.
Requirement include a computer and an android phone running on Android 4.0 (Ice Cream Sandwich) or newer.
Backing up without rooting involve the use of Android Debug Bridge (adb) command

Steps:
Download and install Oracle’s Java Development Kit (JDK) 32-bit version, even if you’re using a 64-bit version of Windows.

Download and install the Android SDK from Google. If the SDK informs you that it can’t find Java, you may have installed the 64-bit version of the JDK – ensure you install the 32-bit version.

After installing Run the Android SDK Manager as Administrator from your Start menu. Enable the Android SDK Platform-tools check box and click the Install button to install the platform tools package, which contains adb.

Now on your Android device enable USB Debugging which is located on the Developer Options screen in Android’s settings then connect your Android smartphone to your computer using a USB cable.

Note the path where you installed the Android SDK. It’s displayed at the top of the Android SDK Manager window, next to SDK Path.

Find the adb.exe file in the platform-tools folder. With the default installation settings, the location is: C:\Users\NAME\AppData\Local\Android\Android-sdk\platform-tools, hold Shift and right-click inside it, and select Open command window here.

This is to test whether adb can communicate with your device, run the following command:

adb devices

You should see a device in the list – if you see no devices, adb can’t communicate with your device because its driver isn’t installed properly.

Backing up Device
You can now use the adb backup command to back up your device. To back up everything, run the following command:

adb backup -apk -shared -all -f C:\Users\NAME\backup.ab

This backs up all your installed apps (APK files) and shared storage (SD card) data to the C:\Users\NAME\backup.ab file on your computer.

Replace NAME in the command with your Windows username or provide another location for the backup file.

After running this command, you’ll have to agree to the backup on your device. You can also encrypt the backup with a password here, if you like.

Depending on how much data there is to back up, the process may take some time.

To restore your backup in the future, run the following command:

adb restore C:\Users\NAME\backup.ab

You’ll be asked if you want to do a full restore – this will replace the data and apps on the device with the ones from your backup. If you encrypted the backup with a password, you’ll have to enter the password to restore it.