In the current (until next month) iPhone 6 and 6 Plus, there's a barometer which is primarily used to monitor elevation, such as flights of stairs or hills if you're exercising outside. (It happens, I have seen it on TV.) It can also be used to monitor atmospheric data as well, like the high and low pressure systems that create weather patterns.
Right now this data is being used (if you allow it) by the Dark Sky weather app. If you allow it. In the current version, you can choose to sign up your iPhone to report barometric pressure where you are:
Allow Dark Sky to send off your barometric pressure for better reporting.
So if you live in a place where weather stations aren't close enough to you to be useful, or you need weather from lots of locations to be accurate, this is a great way to get your hands on that data.
There's also a new app that has announced itself on Reddit called Sunshine, which also promises to make use of that barometer to help better report weather. You can sign up for their beta test and see how it works for you.
There are a few other apps that will use the barometer in your iPhone, but they are mostly using it to monitor the pressure where you are standing/exercising to track elevation, not necessarily as a weather data point. Aside from Dark Sky and apparently Sunshine, there aren't a lot of weather apps tapping into that new barometer. Hopefully this will change if the barometer is also included in the next generation of iPhones.