밀당 is short for 밀고 당기는, which literally means "pushing and pulling". It's the power struggle in romantic relationships where couples "pull and push" by giving attention and then withholding it (playing hard to get). If you have ever been in a relationship, you'll understand how that feels.
I'm guessing you watched 우리 결혼했어요 this weekend, since Taemin and Na-eun were talking about it in the last episode :)