In order to play back videos or photos on your mobile device outside of Capture, you must first download the files to your device via Capture. There won't be anything in the GoPro Album on the phone unless you download the files with Capture first. There is no automatic sync functionality.
Here are a couple of images showing how to download files from Capture to your mobile device:
Once you have the file downloaded onto your phone you can find all your downloaded content in a "GoPro Album" in your phones default photo application, typically this is in the "Gallery" application on Android devices, and in the "Photos" application on iOS devices. Here are a couple of images showing where to find the GoPro Album on your mobile device:
From this point you can go ahead and share your photos and videos out to the world however you'd like.