One of the biggest problems for a spacecraft is heat management. Heat, contrary to what people might assume, does not dissipate very quickly in space. That is because there is no air, or matter of any kind, to conduct heat away. Pure vacuum contains no medium for convection to take place in; heat can only radiate as pure EM. So, a starship builds up thousands of degree of heat from general operations, such as running a warp drive or firing weapons; hardly anything is lost, only added. Think of how much a PC can heat a room. This effect could cook a crew alive. One way you could deal with it would be to collect the heat in a disposable material, and eject this material (like a liquid, or solid heat-sink) into space. Presumably the Federation has an even more advanced method of managing heat; not generating it in the first place somehow.
Phasers deal a shit ton of heat damage, like the magneto-hydrodynamic cannons in Mass Effect. In Mass Effect, a molten liquid metal is accelerated to huge speeds by a magnetic cannon, essentially spraying the enemy with a beam of superheated metal. Star Trek also shows this. In Star Trek, we see evidence of entire starships still melting hours after they were hit by Borg weapons at Wolf 359. We also see it during the Battle of Chintoka, where I think a number of ships are seen being slowly vaporised by Cardassian weapons. Science is awesome:
They may be far more deadly to a starship in heat terms than pure kinetic damage; warping and destroying internal systems that pure kinetic damage may not be able to touch thanks to shock dampening. Think of what would happen to a PC if you aimed a hair-dryer at the motherboard. A phaser might disrupt computer cores via heat damage to their circuitry. I think at some point someone in Star Trek describes how horrific phaser wounds are. We see targets having different layers of tissue being vaporised at different rates during the movies and TNG. Presumably, torpedoes still use concussive, explosive force, albeit of a far higher destructive yield than current weapons. But phasers might primarily be a heat weapon, melting rock, flesh and metal.
I think the moving light was meant to be either an energy charge of some kind moving along a bank of emitters, or an actual physical cannon moving along that bank, and converging on the optimal point to fire, before unleashing it's deadly blast. There was a diagram in the tech manual I think.
The way that the stun setting supposedly works, at least in some material, is by sending a charge along the stream of particles to stun the enemy's nervous system. So it's almost like a taser, except the conducting material isn't a wire, it's the beam itself. I think I remember another franchise once had a weapon that worked in a similar way; a laser superheated air to the target, creating a path, then an energy charge travelled down it.
