What is the current payments system you made reference to, the one that Etherium could replace?
What's the difference between say, Venmo, a friend-to-friend payment method, the Clearing House, and Ethereum/ether?
I have a dollar. You have an apple. We want to deal.
1) We can both agree to use The Bank of Venmo. Sure, it may look like an app, but it's Paypal, which is a financial institution like any other. I offer you a contract that entitles you to a dollar from Venmo. Venmo charges me a dollar for the privilege. We're still dealing in dollars, operating under the banking regulations of any country the transaction occurs under, and shows up on SWIFT just like any other banking transaction.
2) We can both agree to use SWIFT, except we can't, because we're not banking institutions and not governed by the bylaws of international finance. So you still have an apple, I still have a dollar, and no sales happens because our current banking system does not allow you or I to act as a financial institution.
3) We can agree to use some form of cryptocurrency (CC$). I send a command to the network to give you the equivalent of a dollar in the CC$ of your choice, which, and b_b is right, is only really of value because of the secondary market of buying and selling CC$. The value of that CC$ is generally volatile and there may be a lot of wiggle between the time I send it and the time you receive it - this is one of the big beefs against BTC at the moment, there's only like six transactions a second that it can handle, which would barely get through Craigslist in a large city, let alone provide a financial backbone for the whole of the world. BUT when all is said and done, the system/network/computer/whatever you want to call it ensures that for one brief shining second, my dollar and your apple crossed paths at the agreed upon rate with no bank standing between us.
But that's not really the interesting part, it's just the low-hanging fruit. Fundamentally, we're not trading dollars for apples. We're trading value for value and value comes in ways far more diversified than currency and finance. Your apple actually reflects, for example, 1/50th of your bikeride to Safeway, 1/52nd of your day at work, and 1/10th of your hunger because you really want that apple. Meanwhile, my dollar represents approximately 42 seconds of mixing crap reality television (a true statistic, by the way).
Let's say I've got my mixing console wired into Ethereum. Let's say you've got your bicycle wired into Ethereum... and so does everyone else. Vast and mythical forces that I don't even need to know about can value my time at the mixing console down to the second and algorithmically remunerate me for my mad skillz. An ad-hoc network of bicycle delivery services could monitor your Ethereum-connected bicycle and credit your bike for the number of miles it travels x the mass it carries factored by the temperature and humidity. Both of these points could actively negotiate on the network in real time and not only hunt for the best exchange between reality television mixing and apples, they could actually optimize the exchange for both of us. Never mind the fact that value can be traded completely without intermediary - the thing that excites nerds about cc$ is its ability to dissolve "money" as a marker and facilitate a true form of non-intermediated commerce.
Right now, of course, cc$ is hot mostly because shady fucks can use it as a coupon for shady shit that you flat out can't do through SWIFT. But hey. VCRs wouldn't exist without porn, probiotics wouldn't be cost-effective without the Soviet bioweapons program and computers as you know them were largely developed for modeling nuclear weapons blasts so it's not like shady starts are uncommon.