The typical USB external battery allows you to power a Raspberry Pi but when the battery stops or starts charging it shuts down the power output, rebooting the Pi.
A USB battery with Passthrough function, allows power to be passed-through without interruption but does not charge the battery. When the battery stops or starts charging, the Raspberry Pi does NOT loose power, it continues to run on battery power.
Finally a UPS function allows running the Raspberry Pi AND charging the battery simultaneously, and when the battery stops or starts charging, the Raspberry Pi does NOT loose power.
The following batteries are reported to support UPS (or Passthrough where noted.) I am not having luck finding any of them on Amazon.
Anker Astro Mini 3200mAh
LogiLink PA0064 Mobile Power Bank 2200mAh
RS Pro 5000mAh
TeckNet PowerZen 2nd Gen 16750mAh