What is the "off-side engine generator" on an A320?
Offside simply means opposite, and it's to do with the AC bus supply priority.

For the A320 the priority is:


Onside, e.g., left engine IDG for AC BUS 1
External power
APU
Offside, e.g., right engine IDG for AC BUS 1, meaning the left engine's IDG has failed or taken offline.