As I said elsewhere, the basic circuit design is ancient, not my work. Search for solar powered bugs using vibrating pager motors. Many use "analog" circuit designs using individual transistors. This one uses IC's and a MOSFET.
A solar panel (many cells, on the sides of the cube) charges a storage capacitor Cstor. A voltage monitor VMon senses system voltage. When there is enough light and the voltage reaches a threshold voltage, the voltage monitor IC turns on an NMOS mosfet switch which switches ground (low side) to a motor. The motor turns a little, discharging the Cstor capacitor, and the system repeats.
The voltage monitor (also called a voltage supervisor or PMIC) has a hysteresis of only 50 mV, which means it turns off again after the sensed voltage Vsense drops 50mV. But the diode Dhold and capacitor Chold form a clever circuit that temporarily holds up the voltage to the sensing pin of the voltage monitor. That increases the time that the voltage monitor output is enabled (low) and effectively increases the overall hysteresis (difference between the system voltage at turn on and the system voltage at turn off.) In other words, the voltage the voltage monitor sees is different than the system voltage Vcc to the motor.
The circuit does not try to store energy through dark periods. There is no blocking diode on the solar panel so the solar panel leaks backwards in the dark. The storage capacitor leaks on the order of one uA. The voltage monitor uses on the order of one uA. The solar cells produce on the order of tens of uA or more.
The Texas Instrument TPS3839 voltage monitor is actually ultra low power, on the order of 150nA. It senses voltage periodically instead of continuously, to save power. But that is moot in this design, you can use other voltage monitors consuming more power. You might want to use another voltage monitor because they are available with a fixed threshold Vth in a limited range. At one time I used a Richtek brand voltage monitor with a Vth of 1.2V and an operating current of a few uA.
See my other blog about tuning the circuit.