iOS has so many new features, it's nearly impossible to list them all, and can even be difficult to remember which ones are new from iOS 7. It can be a little overwhelming. One of the features that I completely forgot about until just the other day was the "Hey Siri" feature.
For those who have never used an iPhone before, Siri is your beloved personal assistant. She's great at telling you the time or weather, finding a local movie theater, getting directions, pulling yup sports scores, and so much more. Prior to iOS 8, you would get Siri's attention by holding down the Home button. A new feature in iOS makes getting her attention so much easier (and safer when driving).
By simply saying "Hey Siri", Siri will awaken and ask how she can help. This works because iOS 8 is constantly listening for that key phrase. It makes anything and everything just a little easier. For example, if I'm driving and want directions to the nearest Apple Store, I would simply say "Hey Siri, how do I get to the nearest Apple Store?" Next thing you know, she'll be guiding you directly there using the quickest route possible. Want to know what song is playing on the radio? Try saying, "Hey Siri, what song is playing?" Siri will tell you that she needs to listen for a moment, and then she'll give you the name and artist, as well as links to download it.
There is one requirement for using this feature... the iPhone needs to be plugged into a power source. This is required because the process of listening for that key phrase does cause a constant drain of battery. This will likely change over time, but for now... it is what it is.
If this feature doesn't work for you, it's likely not turned on. To enable this feature, go to Settings ▸ General ▸ Siri and turn on "Allow 'Hey Siri'".