What exactly does "whispering sweet nothings into one's ear" mean?

it means that someone is telling you something you want to hear and flatters you/plays with your heart strings, but has no real intentions of being with you or loving you.

like if you're dating this douchebag who cheats on you all the time and he tells you sweetly "baby, I love you. you're beautiful to me and I'll change for you...'' and blah, blah, blah, but he has no intention of changing and probably doesn't love you at all.

it's using romantic language to manipulate someone's emotions.

hope that made sense, haha

Whispering sweet nothings means that he's saying romantic things, "You are beautiful. I love the way you look. You make me happy" etc etc. It's flirting in the form of flattery.

saying romantic but very shallow things. like nothing super deep and important just "oh honey you are so beautiful, I love your eyes blah blah blah..."