Most white LED's need a forward voltage (Vf) around 3.5v. Obviously, most power sources are never exactly that, so we need to "fiddle" with the current path in some way so it's more palatable to the LED.
Buck:
The power source voltage is higher than the Vf, so the supply voltage needs to be lowered.
Boost:
The power source voltage is lower than the Vf, so the supply voltage needs to be raised.
There are circuits which can do both, however most circuits are designed for a certain power source (battery configuration) in mind, so they only do one or the other.
Boost and Buck circuits do use some power. How much depends on the difference in voltage it's dealing with, smaller being better. A ballpark range is between 70-90% efficiency. The rest is lost as waste heat.
Direct Drive:
When your power source voltage is in the Vf range or higher, you can skip using a circuit and just use a resistor instead.
Now for the fun part:
None of the above 3 methods of driving are necessarily "regulated" per se. If a buck or boost circuit is just a liner step up or step down, you will get constant dimming in a sloping fashion.
The term "regulation" generally means that something inside the light controls the current provided to the LED in such a way that the output is relatively constant through the discharge. If the circuit is what's called "current regulated" or "voltage regulated" you get a flat discharge so the brightness remains about the same. There may be some dimming (partly dependent on the batteries being used), but it's a big difference.
Some people throw around the term "fully regulated", which generally means that the curve is VERY flat all the way until the battery is very close to dead. At this point, some lights will suddenly just turn off (bad design), while most will very quickly dim down over a matter of minutes, then continue to run at a greatly reduced output called a "moon mode". Depending on the light, this could last for a number of minutes, or a number of DAYS.
Another term often seen is "partially regulated". This can means a number of things, but one common aspect is that the battery choice can greatly affect your output curve. As batteries are discharged, their internal resistance increases. This is worse for some chemistries than others (ie. alkalines vs lithium vs NiMH). Generally, using NiMH or lithium cells will give you a flatter discharge curve, where alklaline will usually give you a sloping one. However, a few lights are capable of giving table top FLAT regulation with alkalines even (ie. Fenix E20 & E01)
And that is where another term can pop up, "pseudo regulated" for direct drive lights. The example of this is in the 3xAAA format, which usually uses a drop resistor to lower the voltage. Using alkalines, you get a constantly dimming output, and some manufacturers even count on you using alkalines for their increased resistance in the system (again, bad design). However, if you use NiMH, since their resistance is much lower, the output will remain somewhat flat for a while before it starts to drop off.
There are a multitude of combinations and permutations of the above methods for driving a LED, but it's probably best if you just asked for specifics or clarification on any parts rather than going into even more detail.
Edit:
I forgot to add why people like regulated vs non-regulated. Let's compare a theoretical light which is capable of both at the flip of a switch. Same LED, same power source.
In direct drive, let's say you get a runtime that looks like a perfect triangle from start to end, with the tail end being at the 10 hour point. A lot of manufacturers would call this 10 hour mark the runtime of "usable light". A common measurement of runtime here is runtime to 50%, which for a triangular discharge would be 5 hours.
Now let's flip the switch to a fully regulated mode. It starts out at the same level, and maintains that level to about 6.5 hours, then trails off in a dim moon mode so you can find some more batteries.
Why would you want one over the other? Well, regulated gives you less overall runtime, it's the same brightness (same usability) for the entire time. Some people don't like how it suddenly dims without much warning, but that's why it's important for a regulated light in most people's opinion to have some sort of moon mode. Direct drive will give you lot of warning of diminishing cells by dimming.
But which is more useful? With regulated, you are confident that once it drops out of regulation your cells are pretty well used up. With direct drive, will you actually use it all the way down to the end of "useful runtime"? With primaries, you don't want to toss cells with a lot of juice left in them, but do you really want to use a light that dim? Most people would get annoyed around the 2/3 mark and just toss the cells for some fresh ones. Also, if you are using rechargable cells on a direct drive light, you run the risk of running them down below the acceptable low voltage and permenantly damaging them.
Regulated vs non-regulated is somewhat a personal choice, but regulated seems to be prefered by FAR here on CPF.
