Hard to tell with such cryptic context, but on-call is the usual meaning (see previous entries in the glossary)

It probably means a period of time or a shift etc. spent on call; you might also find 'standby duty' works here, but it's impossible for me to tell without proper context to work from.

Usually, this refers to a period of time when someone stays at home, but must be immediately available by phone (or bleeper, etc.) to go and deal with an emergency situation if one arises, for example.

This is subtly different from 'standby', which usually means someone is on site, ready to act in the event of an incident.