Oobsidian is a rare resource left behind by gleamy Ooblets in Ooblets. Gleamy Ooblets are a unique form of Ooblet, much like shiny Pokémon from the Pokémon franchise. They have a different color than the traditional Ooblets, and they give off a particular shine to make it easy to spot them out in the wild. They also count for a different slot in your almanac. The Oobsidian they leave behind is a useful resource.
You can find Oobsidian merely by wandering around town and seeing it on the ground. It usually takes a bit of your energy to lift it and place it in your inventory, but other than that, you won’t have to go too far out of your way if it’s available. You can find it in town, but only if it spawns, and it randomly cycles in and out. Some days you can find it, and others you can’t, so you’ll have to return there the next day. Oobsidian sometimes shows up underneath the rocks you destroy on your farm, too.
Alternatively, you can use wishies to purchase Oobsidian. After the second day in Badgetown you will receive daily activities you can complete to receive wishies. You can choose to use wishies earned from completing badges or the daily activities to purchase them. One Oobsidian costs 100 wishies to buy, and you can do this from your Grumboire or the wishywell at the center of Badgetown.