The BitBox02 firmware is bundled into the BitBoxApp which means that in order to upgrade your BitBox02 firmware you need the latest BitBoxApp.
Your current BitBoxApp will show you a banner if there is a new version available.
Once you have downloaded and installed the latest BitBoxApp, go to "Manage Device" and click "Upgrade" in the Firmware section.
You will then see a pop-up showing you the firmware update details. Click "Upgrade"
Next you will be asked to confirm that you want to upgrade your firmware on the BitBox02 itself. Please confirm.
After you confirmed on your BitBox02 click the "Upgrade firmware now" button in the BitBoxApp.
You will then see a statusbar from 0% to 100% in the BitBoxApp and on your BitBox02. Once the firmware upgrade is done, you will have to enter your device password on your BitBox02 in order to unlock it as usual. Done! :)