"Authorised workshops" are a list of workshops that your insurer has approved. You can get a cheaper rate if you don't mind being restricted to authorised workshops only, though be sure to check that the list does give you sufficient options. People who choose this usually drive older cars or second-hand cars that are no longer under warranty.
"Any workshop" means you can go to any workshop of your choice, but this will mean a higher premium on your car insurance. If your car is still under warranty, you may have to opt for this in order to send your car to your dealer's workshop. Otherwise, your dealer may decide that your warranty is void.