Execute in background option can be checked for these Action types:

• Call Apex
• Create Record
• Update Records
• Delete Records

It allows to execute action asynchronously. It may help in case if the action can not be executed in the current context.

If the asynchronous process fails - user won't get error message on page where he is. The error will be sent to the email address that is responsible for receiving background errors (see it in Work Relay Settings > Notification Settings) or to the current user email address. 

When "Execute in background" is selected you can set a gap - time, which system will wait before starting to run the action. Gap value should be in minutes.