The Apple iPhone 6 Plus is the first iPhone to come with optical image stabilization (OIS), and this feature brings quite the noticeable difference when you compare images between the iPhone 6 Plus and the iPhone 6, which lacks optical stabilization. The effect OIS has is of less blur and a sharper, better-looking image - something particularly well noticeable in low light.
One would naturally assume that the iPhone 6 Plus uses the optical image stabilization in video as well, but all obvious evidence suggests the contrary - the OIS functionality seems to be disabled during video recording. How can we tell? Simple, just take any phone with optical stabilization and start recording a video. If you have an iPhone 6 Plus alongside, you would notice that when tilting the phone the other phone equipped with OIS would stabilize the footage quite visible in live view, while the iPhone 6 Plus would not. This factual evidence suggests that optical image stabilization is only used by Apple for still images.
We have no official confirmation from Apple, but here is what the section about optical stabilization on the company's official website says:
Notice that there is no mention of video in this section, something that is quite telling.
What is the reason for Apple not using optical image stabilization, though? Our educated guess would be that Apple was not content with how video appears blurred and wobbly around the edges with OIS, while with software optical stabilization, that effect could be minimized. So even though optical stabilization seems to be disabled, that could be done for a good reason.