Does anyone know why the Mad Hatter gives Alice that look (a this video and you will know whay mean)

It depends on which 'look' you are referring to in this part.
The first one, when Hatter walks into the court and looks at Alice, he shows her what's happened to him, and how much he tried to keep her presence in Underland a secret. Basically, it's a look of 'No one know's your here. I'll give my life to keep it a secret.' and he almost did.
The other 'look' he gives her when he's making hat's basically shows her how much he cares, and all of his emotions for her at once. Personally, it's my paborito shot in the entire movie, besides the Balcony at Mirana's Castle.

I hope that makes sence.