The power supply contains a 5 volt and 3.3 volt regulator. The microcontroller and MAX232 (RS232 Interface Chip) is powered from 5 volts. The SD Card is powered with 3.3 volts.
The power supply is designed to be powered by either the battery or solar panel. When the solar panel's voltage rises higher than the battery (in sunlight), the board is powered by the panel. At night (or any time the panel voltage goes below the battery), the board is powered by the battery.
A current limiting resistor (R27 in the picture) sits in-line with the 5v power supply. On the board, this is a large through-hole power resistor. This resistor protects the 5 volt regulator from overheating by sinking too much power.
Separte LEDs indicate the presence of 5 volts and 3 volts on the power busses.