yes, terminals B3, B2 and B1 should be connected to points c, b and a respectively.
these terminals are used to balance the cells, which is the reason for using a BMS in the first place.
lets consider your illustration, which shows four cells connected in series. assume that each of these cells should be charged to 3V for a total of 12V. when you're using the battery pack, the cells might discharge at different rates due to slight variations in temperature, internal resistance, etc.
lets say, after using the battery pack for some period of time, that the four cells have discharged to [2V, 2V, 2V, 2.5V] (total of 8.5V). you now plug the battery pack into a charger, configured to charge the pack to 12V. the charger will now pass current through the battery until it measures 12V between the end terminals. since the same current is passed through all four cells, we will assume that they are charging at the same rate. in this case, the charger will measure approximately 12V (~12.1V) when the cells are charged to [2.9V, 2.9V, 2.9V, 3.4V]. at this point, the fourth cell is already severely overcharged. this can be especially problematic when using for example lithium ion cells, which are often very sensitive to being overcharged. best case, it could damage the cell, worst case, it could explode.
the BMS monitors the voltage level of each cell individually using the B1, B2, and B3 connections. it can therefore cut power/disconnect the charger when any of the individual cells exceed a certain voltage (in this case, 3V), providing an added protection to prevent overcharging. its use is not limited to protecting against overcharging, but it is one of the main features of a BMS.
(a lot of the above assumptions are exaggerated and/or simplified to aid in explaining the concept)