Master Data Service and how it is used?

I have a question about Master Data Services. I understand how it can serve as a master list of customers for example, my question is, how is this used? Do the transactional systems connect up to this master list and then store the unique identifier of the master list customer so that this unique identifier can then be used in reporting to identify customers between different transactional systems and report on it as a whole?

You can either use the MDS views directly (direct connection), or treat them as sources for ETL to other systems. Depends on your existing systems. If, e,g, you have many systems referring to customer tables, it's probably easier to go the second route. if this is greenfield, then the first option may be attractive. OTOH you have to be concerned about how many systems may be hammering the MDS views.

There's no one-size-fits-all answer