Each element is tied to a certain enemy faction. and their shields is that element. using the element on them deals bonus damage and helps take down the shields much faster.
- Fallen - Arc damage, signified by blue shields
- Hive - Solar damage, signified by orange shields
- Vex - Void damage, signified by purple shields (exception: some Harpies have arc shields)
- Cabal - Solar damage, signified by orange shields
Most of the time you won't need the element to deal damage, but in a few rare cases I've noticed one area so far with Vex Harpies with Arc shields that take damage from Arc attacks, but resist all others (still do damage, just a lot less).
Your primary weapon will usually be Kinetic damage. Your special and heavy weapons can and should have an element. Preferably one of each element so you are prepared for any encounter.
To directly answer your question instead of quoting long winded and confusing reddit posts:
No, upping your light level will not make you more effective in terms of damage on content unless you were previously underlevelled for it, assuming the same weaponry. Your weapon reaches its maximum damage the moment you hit the same level as the enemy upon which you are firing (unless you're using severely underlevelled weapons, see below), and it will stay that way against all enemies you are of equal or higher level to. The only way to increase your DPS is by upping your weapon's attack or getting higher attack weaponry (or I guess unlocking certain armor mods, but that's besides the point).
Sidenote: This does NOT apply to abilities, just weaponry. Your abilities increase in damage as your light amount goes up.
You will, however, benefit from the better abilities that are on those pieces of equipment and the increased armor rating, which will allow you to survive better. You will also presumably have faster recharging abilities due to the higher level of stats on better gear.
The only way level applies to damage, then, is down scaling due to being underlevelled. If your level is below the level of the enemy you are fighting, you take sharp damage penalties, at four levels below you are not damaging the enemy at all (its level will show ??
). There's also a damage penalty if your weapon's "internal level" is much higher than the enemy you are fighting, but that's rarely very useful information. It does, however, mean that you won't suddenly do worse against low level content just because YOU levelled up, if you're still using the same gun.
Best Answer
If you have the first dlc the best location is the "Fist of Crota" mission on Earth — after the Sword bearer spawns you can pick up the sword and run to the next area where three packs of thralls attack — plenty enough for a quick melee chain.
Source: Just did it myself after trying several other farming spots.