to soften a conversation/discussion that is about to turn into a fight OR a fight dodged by a sweet comment.
Jane: Hey Max! Do you like my new hair?
Max: What about it?
Jane: Omg I can't believe you didn't realize!?
Max: Oh you died it blonde! You look beautiful as always my love.
Jane: Aww thanks babe.
Max thinking ("pheww... this is what I call pillowing. ")