In Destiny 1, Bungie introduced a leveling system called light levels. Since the release of the Taken King DLC, players could now level from 0-40. However, players wanted to go over and beyond their player level and there was also a need to determine a players' capabilities when it came to battle readiness. So Bungie introduced gear levels in the form of Light levels. Each gear contains light levels that add up to an average. Therefore, your Light level could be determined by a players gear level. The better the gear they acquired the more combat ready they would be.
Recommended Light level for Strike Missions
the strength of a single piece of gear as indicated in the photo
Light levels would then be significant for players to determine if they could take on certain Strikes based on the recommended light level indicated per Strike. A weekly Nightfall Strike could have a recommended minimum Light level of 280. This system is also similar to World of Warcraft's Gear Level system and posed the same problems to new players. Often times they wouldn't know what their light level was or how to improve their light level.
How to Increase Your Light Level
To be clear, let's separate these two as they can be confusing to some players.
Character Light Level
You character, upon creation, starts off at level 0 and as you play the game you're character will gain light levels up until light level 40. These light levels can be attained by merely playing through the game and its content.
Gear Light Level
a player's total Power level as indicated in the photo
Once your character has reached the maximum character level of 40, players are now encourage to search for loot to improve the overall Power of their weapons and armor. A players light level can be found in the upper right side of your character in the character menu. Highlighted in Yellow/Orange with large numbers beneath the word Power.
This journey can be a tedious and arduous task as players will have to grind Strike missions and complete tasks repeatedly until they receive a piece of gear they've been looking for. Borrowing elements from other RPG games, high-level gear will only have a small percentage to drop and often times relying on a Random Number Generator. Making the success rate of high-level drops feel random but often worth the grind. The Light Level of a player is equivalent to the quality of gear the player has. Each item, armor and weapon has its own light level and the average of those items is what becomes the player's new light level after they've reached the maximum character level of 40.
Light Levels In the Beta
It is unsure if the Light Level system will be back in Destiny 2. During our play test, Our characters seemed to have a fixed Power Level as indicated in the photo above and since the amount of gear that was made available to us in the beta was limited, we were unable to sufficiently test if we could increase our Power level through improved gear. The gear we would acquire all had the same Attack or Defense level of 200.