Telcos are, as ever, desperate to be out of their core business -- shifting bits. They very much want to move "up the stack" to where the money is seen as greater. Although given that telcos are near the top of most nations league table of stock, you've got to wonder at the wisdom of this ambition.
NFV is seen as a way to both reduce costs and to move up the stack.
As far as reducing costs, telcos have made a dreadful error with the design of 3G: installing bespoke high-touch devices. These bring in some revenue for telcos ("header enhancement"), protect the fragile wireless network from abuses such as DoS and scanning, and provide network functions such as NAT. But when you look at the 3G design you'll see large numbers of these boxes, each purchased at a huge margin (because you pay more for box labelled "3G system firewall" whatever is inside it).
So the attraction of NFV for telcos is moving all these expensive 3G systems into VMs, and then managing those VMs economically and well.
Now for the revenue side. The main focus here is enterprises. Want your employees to have secure access to interior resources without the fuss of a VPN? Then same for cloud-delivered services? But also content providers: want a CDN deep in the wireless network so your content is streamed from next to the wireless head-end?
I'm pessimistic on the revenue side. If only because telcos have a habit of stuffing that up. So many telcos tried movie delivery, but then added so many T&Cs on that and at such a margin that it was difficult and expensive to use. So Netflix rolled right over the top of them. So quickly that telcos couldn't organise a response until it was all over. I imagine there will be a few worthwhile applications, but nothing like the revenue streams some people hope for. The tidying of telco 3G networks will be worth it however: mobile networks have a bad habit of going extensively titsup for hours due to failures in high-touch equipment.