For videos on the latest update procedure using Bluefruit LE Connect see:
You can reprogram the Bluefruit LE module itself over-the-air using an Android or iOS phone/tablet. This doesn't reprogram the ATmega32u4 in the Bluefruit Micro, only the BLE module itself. Since its not a common thing to do, its a little challenging to do.
You will need to disconnect/unpower the Bluefruit Micro, connect a wire temporarily between the DFU pin and GND and then power up the board via USB or battery.
The red LED will blink continuously, letting you know it's in DFU mode. Then follow our guide for field updating the firmware