As reported by engadget,
When you open the updated Music Memos, a notification will prompt you to export your recordings to Voice Memos. If you dismiss the pop-up, it will appear in another seven days. Once you complete the process, you’ll find all your recordings in a folder titled “Music Memos.” Provided you have iOS 14 or iPadOS 14 installed on your device, you’ll still be able to use Music Memos. However, after March 1st, 2021, you won’t be able to download Music Memos if it isn’t already in your App Store purchase history.
Apple didn’t say why it’s shutting down Music Memos, but it’s likely that not that many people were using the software. As 9to5Mac points out, the irony of all this is that Apple introduced Music Memos so that musicians wouldn’t have to use Voice Memos. Now it’s pushing those same users back to Voice Memos.