So basically, the concept of ownership of a financial asset (which is itself, an abstraction) is further abstracted, for the purpose of making the system more efficient.
Fun fact: After Hurricane Sandy in 2012, the DTCC had to recover/restore many damaged paper certificates after their securities vault was flooded. I don't know whether these had any electronic entries but I assume they did. But the physical certificates still needed to be retained.[2]
If you're interested in this sort of market structure/market participant discussion, I'd recommend the textbook Trading and Exchanges: Market Microstructure for Practitioners, by Larry Harris.
0. https://en.wikipedia.org/wiki/Depository_Trust_%26_Clearing_...
1. https://www.bloomberg.com/view/articles/2015-07-14/banks-for...
2. http://www.dtcc.com/annuals/2013/superstorm-sandy-recovery/i...