These are flexible flat cables (FPC) that allow for a microSD card slot to be moved to a more convenient location.
They solve the problem of restricted physical access to a microSD slot, especially when it is embedded deep inside a device with no room for manual insertion or removal.
The cables pass the signals between the device and the microSD card without modification.
They are commonly used with tablets, mobile devices, GPS, car DVDs, and DVRs where the original slot is hard to reach.