폼 means literally form - visible shape, style, design and a particular way etc. .
But it has other meanings
- an ironic or humorous behavior
- describe someone starts something or get prepared.
(폼을 잡다: put on airs or pompous air)
Ex) 새 안경을 사서, 폼 한 번 잡아봤어요.
I bought new glasses, so I put on airs.
아마 Kenny는 지금 낮잠 자려 폼 잡고 있을걸.
Maybe Kenny get preparing a nap now.
날 can be used in expressing something special days, as it is added at word's back.
Ex)
어린이날 ( Children's day )
한글날 ( Hangul Proclamation Day )
오늘은 좋은 날이 아니다.
(Today is not good day.)
날 also is a shortcut for 나를.
In your sentence , it is used as the meaning of "Day" .