Usually you still need a resistor after the transistor to protect the LEDs. However a store bought string may have these resistors in-line already.
The resistor is there to reduce the current to the LED's so they don't burn out. Yes the light will be less due to the "limiting" resistor, as it's called, but without one, that increase in brightness you get will only last for a very short time (sometimes milliseconds) before the LEDs will never light again.
Conversely (and I've seen this done which is why I mention it), thinking that you could use a lower amperage power supply to send a current closer to the theoretical current you would get using the larger PS and a limiting resister together, doesn't work either. Those LEDs will take as much juice as they can, and will attempt to pull too much power through your lower amperage power supply. If there is no fuse in the mix, you could burn out your power supply.
Think of the power supply amperage as the size of a pipe water is running through. The diameter determines how much water you can get out of that pipe. It doesn't mean you always have to open the valve full tilt - a little can always trickle down a big pipe. But it does mean if the device on the end needs more water than the pipe can deliver it will crumple the pipe in it's attempt to suck too much through it. That resistor acts as a check valve (or more accurately, a much smaller but stronger pipe that wont crumple ) to only let so much of the flow through regardless of how much the LEDs are capable of gulping down.
As for the transistor protecting the output (I think this is what you mean), the transistor is a low voltage/low current device (at least at the base leg) . With the right one, the arduino pin will safely send far less power than it's capable of to the transistor base, in a way, protecting the arduino pin or output. The transistor is our heavy lifter here. They are capable of funneling huge amounts of power between the emitter and the collector, even though a trifle is being sent to the base by the arduino. And generally the power being sent from emitter to collector never touches the pin of the arduino, so you are safe there. You have to pick one that is robust enough to handle the current of the LED string (between E and C) and sensitive enough that a range of voltages (0-5v for a standard arduino pin) will trigger the Base pin.
Ideally, in the transistor specs, the emitter/base voltage will be the same as the top voltage the arduino can put out. But this value must always be equal to or higher than the max voltage you are going to send out of the arduino pin, or you can burn out the transistor.
And the emitter/collector amperage spec must be higher than the expected max current the LED string will draw. The voltage of this spec must also be higher than the voltage you are using but this usually isn't an issue since the maximums here are usually up in the 30 to 50V (at least for the BC337 that Paul recommended).
One last consideration (that doesn't really apply here, but just FYI) is how fast the transistor is. Remember the output of the arduino is flashing on and off really really fast - you generally need an oscilloscope to see it its so fast. That transistor has to be able to keep up. It has to shut the power on and off in sync really fast so that the LED string looks like it's dimming and brightening as the time of the "on" cycle gets longer and shorter. The reason it usually doesn't matter for this kind of work is that the speed that the arduino can blink that output (with normal analogOut code) is usually far slower than most transistor's specs. But depending on your application, it can make a difference.
For the final spec on the transistor we really need to know how much current that string wants to draw and which arduino you have. A standard Uno will have a 0-5v output at the pin, one of the new small ones may use the new 3.2V output level. I've even got one here that outputs only 1V at each pin.
