Legendary Shards are a form of currency in Destiny 2, used to infuse and upgrade your weapons and gear, and purchase exotics from the snake-faced bastard Xur. Simply put, you can never have too many of 'em, which is why most players usually have their eyes open for new and more efficient ways to get it. And, as of time of writing, there's currently an exploit that was introduced with the Guardian Games event that is enabling players to generate an infinite supply.
As YouTuber Cheese Forever explains in the video at the top, the method is actually quite simple. First, collect a Guardian Games class item from Zavala in the Tower. This will unlock it in your collection manager. Go to Collection / Armor / Events and find the class item at the bottom of the second tab. Note that last year's version will not work, you have to use this year's.
Now stock up on the class items (the most you can carry is 10 at a time), and then dismantle them. Each one will net you 4 Legendary Shards and 3 weapon parts. Because they only cost 3 Weapon Parts and 250 Glimmer, you will easily turn a profit. Note that to acquire more Glimmer, you simply visit The Spider on The Tangled Shore and purchase it using whatever material he's asking for on the day.
The loop becomes infinite because you can use the Legendary Shards you're making to stock up on those materials. And for that reason, Bungie is bound to hotfix it soon, almost certainly stopping the dismantled items from rewarding Legendary Shards, which appears to simply be an error.
Our own Destiny 2 expert Tim Clark tested the system, and discovered that it works exactly as advertised. He also said it's "incredibly boring and time consuming," but such is the cost that true dedication demands.