According to Gizmodo, it's basically an app that makes it easy for people to cut and paste text and then spam an inside joke on Tiktok:
Don’t think too hard about it, it is what it is.
As it turns out, the tool that they’re using to spam their pals is the Paste Keyboard. On TikTok, right now, there are entire tutorials laying out how to use the app. There’s a fair share of YouTube tutorials, too. Having downloaded the app myself, I can confirm that it makes spamming walls of text at people really easy. Instead of combing through forums (or your notepad app of choice) every time you want to pull up that obscure spam to send your friends, the keyboard just saves it for you. All you need to do is pull it up, tap the Pasta you want, and you have an entire wall of text, ready to go.