If you tell a child you will kiss a part of the body that hurts better, you mean you will make it feel better by kissing it.

"Mummy, I hurt my knee." "Come here, darling, and let me kiss it better." “妈妈，我的膝盖受伤了。”“过来，宝贝儿，我亲一下就不疼了。”

He fetched a dressing for the cut on George's thumb, and bent to kiss it better.

I'm a little bit old, Mum, for you to offer to kiss my banged-up elbow better.

Mummy, can you kiss my boo-boo all better?

You'll be fine once Daddy's kissed it better for you.

See also: kiss verb