A workflow defined as running in the background means the workflow process is executed asynchronously on the CDS platform. Depending on what other background processes are running or the volume of queued processes, a background workflow may be executed within a few seconds, or it could take several minutes.
A background workflow is triggered when a record is newly created, or an updated record is saved, or a record is deleted. The form the user is on refreshes and they can carry on working while the workflow is running. This means that the user will need to refresh their screen to see any results of any steps that the workflow performs.
An example where this causes confusion for users is where a background workflow is run on creation of a record and the workflow creates a phone call record. The user creates a record and does not see the phone call in the timeline until they exit the record and reopen it, or if they press F5 to refresh their browser...