A "flat" is an apartment, or living quarters. You group them in "blocks" because... well, in a group, they look like a block. Don't forget that "flat" must now become plural! "A block of flats". "I sold my house and moved into a block of flats."

a block of fat? I've heard of a chunk of fat, but I've never really heard the expression a block of fat.

a block of flats in the British Word for an apartment building

a block of flats = 一栋公寓楼