Why is light level important in Destiny? How does this work?

As noted by Destinypedia:

Light is a player attribute that boosts the player's level past 20, increasing the damage done by subclass abilities against higher-level enemies. A player's Light can be increased by equipping armor that boosts it.

Because rare armor only gives a maximum of +15 Light per piece, the highest level attainable without Legendary or Exotic armor is 24.

Source: Destinypedia - Light

This will shed light on the question at hand: http://www.reddit.com/r/DestinyTheGame/comments/2h9t6b/this_is_how_light_levels_affect_your_gameplay_and/

It's very simple, you do less damage and take more damage from monsters that are higher level than you. That is why it's important that you're at least lvl 28 when doing the raid, since the mobs are lvl 28, you will do less damage to them if you are below lvl 28

here's a very simple test I conducted (my guardian is lvl 28):

Buy or obtain white/green/blues so you can change your light level (in this case I had gear where I could change my level to 21, 23, 24, and 28)

Do any story mode at lvl 24 heroic (note, the mobs are lvl 24)

equip your gear so you're lvl 28, take ONE shot at a mob and note the dmg (383 with a legendary lvl 20 hand cannon in my case to an acolyte)

equip gear so you're lvl 21, take ONE shot at the same type of mob with the same weapon (I did 184)

equip gear so you're lvl 23, take ONE shot at the same type of mob with the same weapon (I did 261)

equip gear so you're lvl 24 (same lvl as the mob) take ONE shot at the same type of mob with the same weapon (I did 383)

final results doing damage with the same EXACT weapon at the same TYPE OF MOB (lvl 24 acolyte) by just changing my light level

Light 21: 184 dmg Light 23: 261 dmg Light 24: 383 dmg Light 26: 383 dmg Light 28: 383 dmg as you can see, your damage SCALES DOWN TO THAT OF THE ENEMY if you're higher lvl than it (that's why your bullet damage text is grey) and you do reduced damage if you're not the level of your enemy (the same goes for your armor, it scales down to your enemy and you'd take the same damage at lvl 28 as you would lvl 20 from a lvl 4 mob on earth, this is harder to test but trust me, I've done some visual tests and confirmed it)

you can only do damage to mobs that are no higher than 3 lvls above you and you take a penalty in damage for it (that's why you can't even choose a lvl 28 mission if you're lower than lvl 25, you wouldn't do any damage)

4 lvl or lower below mob: 100% damage penalty 3 lvl below mob: ~52% damage penalty 2 lvl below mob: ~42% damage penalty (guesstimate since I didn't have the gear to put me to lvl 22) 1 lvl below mob: ~32% damage penalty 0 lvl below or higher than mob: 0% damage penalty TL:DR your light levels affect BOTH your damage output and how much damage you take only UP TO the level of the mobs (i.e. if you're lvl 28, you'll do the same damage and take the same amount of damage from lvl 20 mobs as you would from lvl 24 mobs, there is ZERO difference)

so in conclusion that is why it's so important to be at least lvl 28 in raids and as I stated in my original post, lvl 20 bounties would be EXACTLY the same as lvl 4 bounties from earth... there is no difference (as long as you're lvl 20+)

this is also why those lvl 24 strike playlists used to be hard at lvl 22, but aren't anymore at lvl 24+, it's because not only are you taking less damage (capped at what you were taking at lvl 24) but you're also doing more damage even though you're using the same exact weapon

this is also why you die as fast doing earth lvl 4 missions as you do doing lvl 18 mars missions even though you're lvl 28 with 1400+ armor, it doesn't matter up to the level of the mobs

An important point which isn't mentioned by these answers is that you can only start missions, strikes and raids that you are within three levels of. This applies separately for each level of difficulty, IE a level 25 Guardian can participate in the level 22 and level 28 Weekly strikes, but cannot participate in the level 30 Weekly strike.