What is the point of R2 in the following diagram: 
I get that R1 controls the current to the Base, but what does R2 do?
Answer
The R2 resistor is used to bring the voltage on the base into a known state. Basically when you turn the whatever source of current you have at the other side of R1 off, the whole line would go into an unknown state. It may pick up some stray interference and that may influence the operation of the transistor or the device on the other side or it may take some time for the voltage to drop just with just the transistor base. Also note that the source of the current going through R1 may leak and that may affect the way transistor operates.
With the R2, which is in configuration called pull-down resistor, we are certain that whatever excess voltage there may be in the branch containing R1 will be safely conducted into ground.
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