Here's how I've been explaining it recently:
1) There's a business that Ripple has providing transaction processing software to banks. It can work without XRP and without any blockchain tech. It improves international payments because it uses end to end messaging to track payment progress, ensure all necessary compliance information is in the transaction in the first place, precisely knows the fees ahead of time, and provides prompt, reliable confirmation of delivery. This is a big enough improvement that banks will use it even if the actual money moves the same way it does now.
2) Ripple has built a public blockchain with a native asset. It has various nice features -- a distributed exchange, good governance, fast transactions, high transaction volume, native multisign, key rotation, payment channels, and so on.
3) The hard part about getting banks to use a blockchain isn't the blockchain, it's everything else. It's governance, compliance, integration with banking systems, and so on. our software does all that stuff, so if routing a payment through XRP is a penny cheaper, the bank can take it. Then we have to make XRP cheaper somewhere that matters.
4) We don't target the biggest corridors like USD->EUR because they're efficient. We target an inefficient, but fairly high volume, corridor. For example, EUR->INR. Market makers have very small profit margins, so even a small incentive to place good EUR<->XRP and XRP<->INR offers can beat what banks are getting now through the correspondent banking system.
5) Once we get one corridor, we hang other countries off each end of the corridor, expanding the reach of XRP.
6) Now, say you're a company like Seagate that pays out money all over the globe. If you have to make payments to five countries in our corridors, you'd rather hold one pile of XRP than five piles of different currencies. That increases demand.
7) Now, say you're a company like Apple with a huge pile of cash. If you want to snap up other assets cheap, you'll need to hold the asset the people selling want. If they're going into any of our corridors, they'll want XRP, so you would want to hold it.
8) If that succeeds, it should massively increase the price of XRP.
9) Ripple holds a huge pile of XRP and will be the dominant XRP holder for the foreseeable future. But we're primarily VC financed and we get revenue from selling software to banks. We don't use our XRP as a bank account but as a strategic weapon. (Though we do sell some for revenue, we just don't need to for salaries or to keep the lights on.)
10) Anyone who gets XRP from us as part of some deal with a lockup has their incentives aligned with ours. They want the long-term price of XRP to go up too.
I think that pretty much covers our vision. There is, of course, no guarantee of success. This is a pretty crazy thing we're trying to do. But we have 160 full time employees and have raised tens of millions of dollars. We've hired many amazing people, and our track record speaks for itself.