Enhancement Cores are an important part of Destiny 2. Their sole purpose is to upgrade Legendary items (purples) into Masterworks. Masterwork weapons sit between Legendary and Exotic items (yellow) and can be created through upgrades, or found as drops.

To digress a little, there's three key things to remember when it comes to Masterwork weapons - and why you should be farming Enhancement Cores:

• Kill Tracker: Masterwork Weapons come in either a Vanguard or a Crucible variation. The Crucible ones will track PvP kills with the weapon, while the Vanguard ones will instead track PvE kills with the weapon. The kill stats can be checked from the inventory screen, by hovering over the weapon's icon. (Note: the kill trackers do not take into account kills from before the weapon was made into a Masterwork or switched from one Masterwork type to the other.)
• Orbs of Light: Masterwork Weapons generate Orbs of Light on multikills (specifically, whenever 2 kills are made with little time elapsing in between), which allow both their user and their teammates to charge their Supers at a faster rate.
  • The weapon's user will create small Orbs of Light for themselves, at the location of the enemy.
  • The user's allies will find large Orbs of Light, at the location of the user.
• Additional Stat Node: Masterwork Weapons come with a special Modification slot containing a stat bonus. The bonus can be rerolled in exchange for 3 Masterwork Cores and 25 Legendary Shards to change which stat is bonused.

To gain the Masterwork bonuses (worth it for Orbs of Light), you need Enhancement Cores, and need to upgrade your weapon of choice multiple times. This doesn't come cheap, and the cost of Enhancement Cores is around 5 at the final stages. With that in mind...

How To Farm Enhancement Cores Quickly

There's a couple of options here.

1. The first, and most common method, is to go and trade with the Spider in Tangled Shore. You can exchange your Legendary Shards for Enhancement Cores, though you should limit this to two per day.

2. You can buy Simulation Seeds from Spider, and take these to Brother Vance on Mercury to turn in, and obtain Engrams. Doing this will allow you to gain a significant amount of Legendary weapons, which you can then dismantle for a chance at Enhancement Cores (as well as more Shards, to trade with The Spider). 

3. Your next best alternative, is to run any Raid and should a Masterwork weapon drop, just dismantle it for a significant chance at multiple Enhancement Cores.

4. Finally, you've the option of some Bounties from the Gunsmith at The Tower or Spider himself. Both offer daily Bounties that reward Enhancement Cores which, when combined with material exchange from Spider, should give you enough for at least 7 per day.