It's abstracting above having to manage and think about servers. Just as most developers stopped having to think about registers or print drivers or low-level network protocols or memory pages. You still have all these but you gain big by having technologies that let you abstract away from these levels of detail. Buzzwordy, yeah sure. But the meaning and implications are pretty powerful.
Except it doesn't really. You still have to deal with the important things. All that's removed is the tediousness of the physical server maintenance. You still need to architect for redundancy, deal with latency, client/server caching, etc. Your app cares just as much about the server as it always did and your server-side code needs to be as robust as if it were running on dedicated hardware (perhaps more robust).
And as wmf pointed out, we already have plenty of buzzwords for this. PaaS, IaaS, "Cloud computing", etc.
