Can someone explain the battery management schematic for the following robot?
As the supporting text states, it's setup to monitor cell voltage. It can trip/trigger an alarm if/when the cells get out of line (too large of a voltage difference between cells). If the voltage difference is too high then you run the risk of overdraining or overcharging cells when you draw/charge based on total pack voltage as total pack voltage winds up giving you an average per cell voltage value. 

Over discharging will permanently kill a battery quick, but over charging the battery, especially lithium batteries, could at best physically damage the battery and at worst start a fire or even explode. 

To get the cells back inline (equalize voltages), it looks like the circuit is setup to simply bleed off excess capacity through some power resistors. As all batteries have a relationship between state of charge and voltage, if you change the state of charge you can change the battery voltage. Once all cells are in line (same voltage), charging to maxixmum capacity ensures all batteries are fully charged and none are overcharged. 

As a side note, you can't really get all batteries exactly equal, so you should never charge all the way up to 100% - stop around 95% if you feel good about your battery management system or 90% if you don't. Also note that you can't get a good gauge of state of charge by measuring terminal voltage unless the batteries have had an adequate period of time to rest, generally about 8 hours for lithium batteries.