What is the "-rescue" function of Clonezilla and when should I use it?

The -rescue option is meant to "Continue reading past block read errors." as per this manual.

This means that it doesn't stop when it reaches a sector error. It simply ignores or bypasses them, enabling you to pull off as much data as possible.

If the option isn't selected, CloneZilla will halt and throw a warning message like the one your received.

Therefore you must be extra careful to validate the extracted files for errors. Binary files such as executables and libraries should consequently be dismissed or updated with a reliable version.