Coloquially, the duration required for a system, application, service or hardware to get from fully operational and ready state to a halt- or off-state.

Shutdown time can be important in critical situations. For example a database containing secret data or a sensitive service is attacked, their access compromised. That could mean that unauthorized or malicious parties might get access to sensitive or secret information. In such a case, it might be required to get that data or service out of the line-of-attack as quickly as possible in a controlled (and hopefully non-destructive) manner.

Related to startup-time