In simple economic terms it allows Saints (as they are known) to participate in the global digital economy. Both as providers (everything from programmers to call centres) to consumers (basic things like voice,meetings,streaming etc.)
St Helena now has an airport so with connectivity, tourism also improves. Its a lot easier to take a week to visit a truly exotic location if connectivity is also good.
Currently the islands share a small satillite connection, which is very expensive, and very slow.
In summary, the provision of good connectivity in rural areas helps stem the flood to ever larger urban areas, and allows remote communities to both preserve themselves but also participate directly in a global economy.