At the moment if you want to use an app on your Apple Watch it is actually running on your iPhone and being transmitted over to your watch. This is because Apple have not yet opened up the SDK to developers but this may be set to change in the very near future.
Apples SVP of operations, Jeff Williams, has revealed that this SDK will likely be released at WWDC this summer. This will allow developers to make apps that will run solely on the Apple Watch with no need for your iPhone to be nearby.
This will be a big improvement for the Apple Watch as it will allow for much better performance from apps and will also allow developers to make full use of the Watches sensors.
This will also have an affect on battery life. These apps will be using more of the processing power of the watch so therefore the battery life will decrease. On the other hand this will mean that the watch doesn’t have to use the phones processing power so the battery life of your iPhone should increase.