It is a bit difficult to explain this without more context. You have to do an action or movement and simultaneously make the cutest sound that you can do.

Natasha, when possible, include the URL (web address) in your questions. I think I found it. http://www.soompi.com/2015/06/15/lee-seo-jun-stays-behind-to-clean-up-the-mess-he-and-his-brother-made-on-superman-returns/ It's about babies. "Cute" means "adorable" and "sweet"--in the way babies are. You could say "Aw! Isn't he cute?" With babies, it is common to use exaggerated superlatives. " or "Aw! the sweet little darling, he's just the most precious thing in the world, he's the cutest thing ever." "The cutest sounds possible" means he is making very cute, adorable sounds. "The cutest sounds possible" literally means no baby has ever made cuter sounds, no baby will ever make cuter sounds.