Actually, this is a current regulator, not a very good one as many might judge, but one none the less.
Consider the base circuit for a minute. Three NiCd cells will make a battery of say 3.75 Volts. If the Vbe of our (silicon) transistor is .7 Volts, there is is 3.05 Volts 'across the 680 ohms'. 3.05 divided by 680 is 5.25 mA for base drive. The Beta (DC current gain) of typical small signal bipolar transistors is probably some thing like 30 to 50 at these sorts of levels, let's assume 40? Forty times 5.25 mA is 206 mA, this is the current in the collector circuit, provided Vf of the LED and Vbat don't force it into saturation (basically zero volts from Collector to Emitter). In practice .25 Volts is probably about as close to saturation as we can expect unless we pick a low Vsat part, meaning that we need the Vf of our LED to be under 3.5 Volts at 200 mA (which it should be).
Due to the relatively large voltage across the resistor, small changes in Vbat will cause only very small changes in Ibase, therefore very small changes in LED current, far smaller than a simple resistor with a fraction of a volt would cause. Changes in Vf of the LED will not change the current at all, unlike the simple resistor circuit (unless it gets much bigger of course), 'thermal runaway' (at least from the LED) is not possible here, but a very real problem with the simple resistor. Beta does go up with transistor temperature, but it should stabilize quite quickly (at least it did when I *tried* this suggested circuit......).
Once the value of the single circuit is 'selected' against the transistor and battery used, it should be far more stable than a simple resistor circuit.
There's a bit of well intentioned but incorrect advice in this thread. Those who would say 'this is no way to bias a transistor' must not have any formal training. It not only is a very common scheme, but being the simplest is the first method taught. Most every class A stage in cheap transistor radios (say the IF strip) is biased this way. While far from optimum, it's the simplest and therefore has a place. FETs have *gates* that respond to *voltage*, bipolars have *bases* that respond to currents. The one type of JFET that will work here, N channel enhancement mode devices, are very marginal at this low a gate voltage, most needing a bit more than 4 Volts to guarantee 'turn on', which is just what they'll do (go from no current to 'full blast'). No current regulation, a simple switch in a 'direct drive' LED circuit. Changing the resistor value will have no practical effect. As 'stiff' base supply (as suggested using a zener diode) will work *if* we also add a low value resistor to the emitter circuit so that Vbe plus the voltage drop on the resistor at design current equals Vz, but we'll need more battery voltage and an extra resistor.
The circuit is simple to the point of being primitive, but it does regulate. And it's simple enough to actually build so you don't have to guess about what goes on. Like I said, it seems I might have an unfair advantage here, not only did it teach this good stuff for a while, but I actually tried it........
Doug Owen