Christopher,
Regulated mean that their is a curcuit that detects the drop on voltage or amperage (or both) and adjusts the regulators output to keep the electricity to the LED stable. To make it simple.... and assuming 100% effeciency (they are more like 80 to 90%) Say the LED needs 4.5 volts and 350 milliamps of current to stay at max brightness. Load it up with two batteries for 3 volts and the curcuit will boost the output to a regulated 4.5 volts and 350 milliamps of current.
How it does it is it draws extra amperage at 3 volts (525 mA in this case) to put out 4.5v at 350 mA. Now, when the batteries start to discharge and drop down to say 2 volts... the regulator draws more current to keep the voltage/current at correct levels. To get 2 volts up that high it would draw 788 mA to get out 4.5v and 350 mA.
In reality... the curcuits are not perfect and eat some electricity when they make the conversion. The Badboy 500mA regulator is rated at 82% so the other 18% is used to regulate and it is given off as heat. In the real world, the regulated light would draw more than 788 mA of current at 2 volts to keep the output steady. Regulated lights will run hotter for this reason. They also will eat batteries faster but, in my use... I will get over it!
Anything that regulates or converts electricity to different levels or converts AC to DC or DC to AC will consume power doing so. The power supply on your computer is an easy way to check it out. It changes either 120 volts AC or 220/240 volts AC to 12 volts, 5 volts and 3.3 volts DC (some rails are negative or positive) They usually eat around 25 to 35% of the power changing it over and that is given off as heat. Hence the reason that fan is blowing over the heatsinks to cool them down. Those DC power supplies (wall warts) that run small computer speakers and the like do the same thing. You will notice that they give off some heat also.
The advantages of regulators is they will keep the LED fed the right diet... the downside is they will eat off the battery plate themselves so there is no free lunch. The "direct drive" LED lights start off bright but then start to get slowly dimmer as time marches on. That is why some of those 3 D cell 1.2 watt Luxeon star lights will give off light for days at a time... not maximum brightness but will use what energy they can find.
Hope that answers a few of your questions, have a great day and try out both "direct drive" and "regulated" lights to see which ones you like the best.