어제는 철수 씨 생일이었는 줄 몰랐어요
The basic structure is
어제는 몰랐어요
Yesterday, I didn't know
The whole sentence means
Yesterday, I didn't know that a certain day was Cheolsu's birthday.
어제가 철수 씨 생일이었는 줄 몰랐어요
The basic structure is
(저는) 몰랐어요
I din't know
The whole sentence means
I didn't know that yesterday was Cheolsu's birthday.