The circuit board looks like a motor driver, there are loads of versions of these, so getting the correct one won't be straightforward, you need to find out what type of motor, and what type of signal is used to switch it. Once you have done this e bay has loads, so look there, the cable connection looks like a fairly standard two wire with JST2 plug at one end and plain/straight crimps at the other.
In the other photo, this is a power board, basically you plug a JST2 cable as above in to one socket (the other end to your battery or power supply) and then feed a number of other things using the other sockets as outputs so for example using a JST2 to JST2 cable from the power board to your motor driver etc.
The idea is just one connection to the battery, rather than everything having to be connected together at the battery