Looking at the user guide, it looks like this is a way to have the switch participating in multiple STP domains on different ports where there's a need to have different source MAC addresses (not have every BPDU leaving the switch with the same source MAC - which may confuse other devices in the network).
I can't personally think of an exact use case for this, but it is one of those tools that could be useful in a troublesome L2 STP problem.
This is also a slightly unusual definition of setting a Locally Administered MAC - I would normally interpret that feature as something which let you globally set the MAC address of the switch. That has two use-cases that I can think of:
1) Your organisation has its own block of MAC addresses from the IEEE and you use these in production (maybe for VMs or something) and you have a policy to use them on networking equipment too. Slightly unlikely, I agree, but possible...
2) You need to swap out a switch acting as a router connecting to 3rd party systems, and they have a MAC lock on your port. This is common at Internet Exchanges, and if you have a failure in the middle of the night, it is sometimes easier to just configure the MAC address of the new switch to match the old one to stop port security problems.
Paul.