Crystal Core is the item that you get whenever you catch a butterflies. There are different color butterflies, but they all drop the same item. The Crystal Cores are used to craft the new item coming in patch 1.1, which is the Condensed Resin.
Crafting Condensed Resin
To make Condensed Resin, you need to get the blueprint by reaching reputation level 3 in Liyue. Then go to the crafting table and use the required materials. It takes 1 Crystal Core, 40 Original Resin, and 100 Mora to make 1. You can only have a maximum of 3 Condensed Resin at one time.
Condensed Resin Uses
Condensed Resins can only be used on Ley Lines and Domains reward drops. Using 1 Condensed Resin will give double the rewards since it costs 40 to make 1. Both sets of rewards will still be random, so using it on domains won't mean you get 2 of the same artifact drops.
East of Mondstadt is the Windrise area. You can find about 4 butterflies near the tree that's close to the Statue of the Seven.
Mt. Tianheng, west of Liyue Harbor, has a small cave with about 6 butterflies in the area, as well as some Noctilucous Jades. It's not far from the closest teleport waypoint.
You can find about 4 more in the cave that's further west of Mt. Tianheng. Most of the butterflies here are close to the entrance of the cave, so you don't really need to go further inside, but there is a shrine with some farmable ores.
East of Liyue Harbor is the Guyun Stone Forest area. There are 4~5 butterflies just in front of the "Domain of Guyun" entrance.