The async option will send the script to the system scheduler, and it will be run shortly after the record is saved. This option is good for when the script you have written does not need to be run immediately after the record is saved.
Good uses for the async option are for sending messages between integrations and sending tasks to the ECC queue. Remember that the async option can have a more significant delay if the ServiceNow instance-scheduled job queue is long, so be mindful of the average wait time for your instance when setting an async business rule. If you would like a more instant running of your script, consider the after option.
