There are G sensors connected to a small computer, battery, display and usually some Bluetooth for the link.
This would make for your basic activity sensor rig. How it syncs with android/iOS is usually over a link. Said link can be wired or wireless.
If you want to go deeper take a few courses in electronics and embedded computing. If you want to dive into this without that look up the Arduino kits and what sensors you can add to that.
does anybody know what technology/sensors are intalled inside fitness wristbands and how do they interface with smartphones? Are those sensors syncing just with android/iOS or they have an open API? Your help will be appreciated!