Disclaimer: This entry is, among other things, an expansion on my reply to
this comment on a friend's LJ.
All right, first, let's get some definitions down. According to Wiktionary, the definition of "machine gun" is: "A type of firearm that automatically fires bullets in rapid succession." Note the adjective; a rapid-fire firearm that does not fire automatically is not, by the dictionary definition, a machine gun. The military definition of a machine gun is a fully-automatic weapon that fires rounds of a rifle or more-powerful chambering and is designed to be fired from a support (vehicle mounting or tripod) rather than as a hand-held weapon.
The legal definition of a machine gun, per the
National Firearms Act of 1934, is "any weapon which shoots, is designed to shoot, or can be readily restored to shoot, automatically more than one shot, without manual reloading, by a single function of the trigger. The term shall also include the frame or receiver of any such weapon, any part designed and intended solely and exclusively, or combination of parts designed and intended, for use in converting a weapon into a machinegun, and any combination of parts from which a machinegun can be assembled if such parts are in the possession or under the control of a person." (US Code, Title 26, Subtitle E, Chapter 53, Subchapter B, Part 1, Section 5845, Subsection B.) Historically, the courts have ruled that hand-cranked Gatling-type firearms are not, legally speaking, machine guns, as the continuous hand-cranking is not "a single function of the trigger;" electrically-driven ones, however, are, as they fire continuously as long as the trigger is held down.
This also means that, legally, an M16 is a machine gun, while an AR-15 (the only difference being that the AR-15's selector/safety does not include a position permitting fully automatic fire--which is literally just one different cam) is a rifle ("a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder and designed or redesigned and made or remade to use the energy of the explosive in a fixed cartridge to fire only a single projectile through a rifled bore for each single pull of the trigger, and shall include any such weapon which may be readily restored to fire a fixed cartridge").
Fully automatic operation of a firearm is, of course, a system where, when the trigger is depressed, it will fire the currently chambered round, automatically reload itself, and then fire the newly chambered round, continuing the cycle until either the trigger is released or the ammunition supply runs out. Semi-automatic operation is a related system where depressing the trigger causes the firearm to fire the currently chambered round and then automatically reload itself, but *not* fire the newly loaded round until the trigger is released and depressed again--technically, this means that a double-action revolver is also a semi-automatic weapon, as the shooter does not need to manually "reload" by cocking the hammer to advance the cylinder to the next chamber.
None of these definitions make provision for a "semi-automatic machine gun;" by definition, a machine gun is inherently a fully-automatic weapon.
Additionally, there is no dictionary or legal definition of "assault rifle" or "assault weapon"; the military definition of "assault rifle" is a fully-automatic weapon chambered for an "intermediate rifle round" (i.e., more powerful than a handgun round, but less powerful than a full-sized .30-caliber rifle round like the .30-06 or the .308 Winchester/7.62x54mm NATO) and designed to be fired in a hand-held position; the term (a direct translation of the German "sturmgewehr," which was a name created in WW2 specifically to fool Hitler into thinking that the StG.44 wasn't the same weapon he'd already ordered--out of ignorance--be abandoned) was coined in the early 1960s to differentiate the less-powerful weapons like the AK-47 and the M16 from traditional "combat rifles" such as the M1 Garand or the M14.
Now, fundamentally, the purpose of a firearm is simple--to have a small piece of metal travelling at extremely high speed pass through a specified point in space selected by the operator, on demand, with as little variation as possible. That's the only thing the weapon itself will do--move a piece of metal very quickly on a predictable path.
More realistically, any firearm is a tool intended to make holes in objects from a distance. While the holes are not always very clean, and the precise location of the hole is less controllable than, say, a drill, but the ability to put a hole in the object from a distance greater than the length of your arms is the key ability. The decision of the material through which the hole is made lies entirely in the hands of the operator--it could be a paper target, a block of wood, a chunk of concrete, a deer, or a person, just as a power drill could be used to bore a hole in any of those items.
What purpose could someone have for wanting to own a semi-automatic AR-15? As
vakkotaur stated in his reply to the post, in addition to killing people, there's hunting and target shooting. There's also the possibility of wanting to have one to hang on the wall as a memory of serving in the military, or to experiment with in an effort to develop improvements on the existing design to market to legal customers, renting it out to movie and/or television producers to use in productions, or even (gasp) being a licensed firearms dealer who keeps it in inventory for potential sale to legal buyers.
The claim of "being excessive for hunting purposes," often trumpeted as a reason for banning various types of rifle is a non-starter. First, it depends on what kind of game you're hunting--a round adequate for hunting squirrel would be completely inadequate for hunting deer; likewise, a good deer hunting round would be inadequate for hunting elk or moose. In both cases, the round would not do enough damage to the larger animal to be effective against it.
Secondly, the most humane hunting round is the one that does enough damage to immediately kill the animal if a hit is scored. Which would be more humane, being killed instantly, or slowly bleeding to death from a wound, and dying days later of infection if the bleeding stops before it becomes fatal? I know I'd find the latter much more agonizing and undesirable. As it happens, the sort of round that will drop a deer instantly is almost identical to the sort of round required to drop a human instantly; this means that .223 is a very widely used deer round. (Think about it--humans and deer are of similar mass, torso volume, and body density, so they have similar requirements.)
The ability to rapidly fire a second shot is of great benefit when hunting, should something unexpected (a gust of wind, a nervous twitch, or whatever) cause your first shot to miss. Long effective range is also desirable, as it reduces the chance of the animal detecting the hunter before he or she takes the shot. Precision accuracy, as Vakko noted, is good both to prevent wasted rounds, and to increase the odds of a first-shot kill by allowing the shooter to accurately target the animal's vitals. Light weight is of value for the simple reason that I'm sure anyone would rather carry a six-pound rifle to go hunting than carry a twenty-pound one.
Other than those regarding the power of the round, all of these arguments also apply to target shooting--and if you practice with the same weapon you use hunting, then that also becomes a non-issue. (Many shooters who only compete in range shooting, by the way, choose to use "low-powered" rounds like the .22LR, because it reduces the cost of ammunition, even using the match-grade handloaded ammunition that they prefer.)
Regarding reinstating the badly misnamed 1994 Assault Weapons Ban, not only did it arbitrarily draw a distinction between the functionally-identical AR-15 and Mini-14 (the latter, BTW, is just a semi-auto-only version of the M14 scaled down to use the smaller .223 cartridge), ironically, the "high-powered" weapons that it prohibited were *less* powerful than weapons left untouched by it, such as the M1 Garand (.30-06 semi-automatic rifle), or the M1903 Springfield (.30-06 bolt-action rifle).
This post is getting long enough as it is, so I won't inject further commentary at this point...