How will the cellular feature of the Apple Watch Series 3 work? If a user goes outside with the Apple Watch Series 3 and keeps their iPhone at home, how will the calling feature work?
The Apple Watch Series 3 GPS + Cellular has LTE built-in. Here are the bands supported by the USA version:


  LTE
  2 (1900 MHz)
  4 (AWS)
  5 (850 MHz)
  12 (700 MHz)
  13 (700c MHz)
  17 (700b MHz)
  18 (800 MHz)
  19 (800 MHz)
  25 (1900 MHz)
  26 (800 MHz)
  41 (TD 2500)  
  
  UMTS
  800 MHz
  850 MHz
  1700 MHz
  1900 MHz  


SOURCE

That same page also lists the bands for other countries.