When does a transistor turn on
First, let's assume the Vf for the LED is ~2V (it can vary depending upon the color of the LED, and the current, etc.). If the transistor is on, the Vbe = ~0.6V. So, if the transistor base voltage, Vb, is higher than 2.6V (2V+0.6V), the transisor and LED are on, otherwise they are off.

The two resistors bias the transistor base voltage. If Vb, without considering base current, is higher then 2.6V, the current into the base can be calculated by Ibase = (9V-2.6V)/Rupper - 2.6V/Rlower. Then Ic = Iled = B * Ibase. If Vb, without considering base current, is lower then 2.6V, the transistor and LED are off.