Basically, the transistor here makes a regulator out of your usual voltage divider.
The problem with voltage dividers is that, if you draw current from them, their voltage output drops down (because the load will act as if there was another resistor in parallel with the bottom resistor of the divider). And their output voltage value will therefore largely depend on the load current, which can fluctuate.
Now, with the transistor here, the voltage at the output will be about the voltage at the transistor base minus VBE (about 0.6V). Moreover, the current flowing through the base (so the current flowing out of the divider) will be much less (beta ratio) than the current flowing through the load. Which means that the current drawn from the divider will be much less dependent on the current through the load, so the voltage at the base will be more or less constant. So, overall, the voltage output will be much more stable.
It still doesn't make a very good regulator, however. There will still be some voltage drop depending on the load current, and, if the input voltage changes, the output will change too. But it can be sufficient in some applications.