I'll take a stab at a very high-level overview by describing a generalized goal, the limitations of Smart Contracts, and the outlines of a solution. This will hopefully provide some context for the implementation details.
1) The goal. A Smart Contract that can react to an observable event or data point in the universe. With so much data sloshing about on the internet, it's natural to contemplate automated responses to things that happen. This is so common outside of blockchains, it can seem surprising that it's so difficult within blockchains.
2) The problem. A Smart Contract can't reach out for data like a typical web server could attach to an API or RSS feed (or screen scaper, etc.) At a fairly deep level, there's a real problem here, because everything on a blockchain has to be verifiable by all miners. Any such external sourcing of inputs would also be a source of uncertainty that would confuse verification. Everything in the chain has to be verifiable not just by one server, but by ALL servers, and not just today. Forever.
How would any node confirm, years from now, that today, at precisely this time, a certain URL produced a certain data stream? If it can't do that, then how would it confirm the truth of the data in the chain? If that's not reliable (it isn't), then things will fall apart. If the blockchain isn't objectively verifiable using only the data in the blockchain itself, it doesn't work.
3) The Oracle solution. We can imagine a trusted person pressed into service (poor guy). He has a privileged account that can inject data he receives from outside the blockchain, and he's depended on to update the blockchain at intervals. Suppose he never sleeps and he updates the ticker data every few minutes.
We can imagine a simplified function along these lines:
function recordTickerData(bytes8 symbol, uint high, uint low, uint close)
// store the data
// possibly react to the data
Great. Only the Oracle is allowed to inject data this way, but once the data is injected, we can start to do things with it, which is what we want.
The miners will be able to verify the blockchain. They won't be able to confirm that the Oracle's inputs match anything in the outside universe, but they will be able to confirm that the Oracle's inputs are allowed, and any resulting transactions are legitimate.
We've got some loose ends to address. First, the Oracle will need to sleep, and this is clearly a job for something automated. Second, every time the Oracle executes this function, he'll have to pay gas for the transaction. That means we'll have to pay the Oracle first so it has some funding from which to pay for the gas.
See where this is going?
Without getting into implementation details, the Oracle will have to resolve the incoming data, from a source, and map it to the contract's interface. There will be details about how often to call the function, and so forth. And there will be the administrative issue of funding since the Oracle will need a continuous source of funding to pay the gas for its periodic data injections. Anyone with serious funding involved will want to verify the Oracle arrangement is trustworthy because its inputs will have non-trivial consequences. So we have a requirement of selecting a data source that will be widely agreeable. We have some broad brush-stroke outlines of generalized Oracle solutions - let's have a trustworthy external service that maps outside data to one of our input functions and periodically sends update transactions.
Opinion markets like Auger and Gnosis present a slightly different take on information from the outside world. Suppose your contract depends on a one-time true/false condition and it isn't obvious that there's an outside source you can know about, in advance, that will transmit a simple truth to your contract.
For example, will Trump win the 2017 election?
Opinion markets provide a way to set up the question and, essentially, outsource the determination of the truth to a human community. It takes the form of a betting market that ultimately settles the question in a way you can configure in advance.
In pseudo-code, your contract can consider:
if(AugurQuestion(123).isDecided and isTrue) then ... do stuff.
I hope the foregoing sets the stage, somewhat, and provides some context to the implementation details of these efforts.