Over the past couple there has been an increasing amount of evidence indicating that some apps (such as Facebook, Twitter, and Instagram) are somehow listening to your conversations and using it to target ads. Facebook vehemently denies this is the case, but I'm starting to have my doubts. People are continually testing this theory and coming up with similar results—namely, they have a conversation about a random subject and then shortly thereafter they start getting ads about that product on Facebook. Vice recently did a story on it, and it's certainly suspicious. Unfortunately, their article is extremely light on technical details, and frankly doesn't make a lot of sense.
Apple keeps your iPhone locked down by default. Apps can only access the camera or microphone if you explicitly give them permission, and they have to list what it's going to be used for. An app collecting data this way would be a violation of Apple's guidelines, certainly, but also would seem to indicate that it's using the microphone in a way it technically shouldn't be able to.
Some of the test results we're seeing from people could be due to improper testing methods and some of them could be due to sheer coincidence, but I'm starting to believe there may be something to it. Knowing a bit about how the iPhone functions, however, leads me to believe that it likely isn't the conduit for this behavior. Many devices have microphones in them, and we already know that many smart TVs have been listening to people. Still, until this is better understood I would err on the side of caution and disable microphone and camera access for apps that don't need it. Here's how:
Go to Settings > Privacy > Microphone and disable it for any apps you don't trust.
Go to Settings > Privacy > Camera and do the same. Keep in mind that some apps use the cameras for things like scanning barcodes. If you turn the camera off, they may lose some functionality (although they'll prompt you if that's the case).
Hopefully someone will be able to figure out what's really going on. I may sign up for Facebook myself (ugh!) just to test it.