서대문 is 'west gate'.
북대문 is 'north gate'.
대 is means 'great'. so your understanding is right.
example,
대한민국 is Great 한국
대자연 is Great Nature.
대우주 is Great Universe.
대가족 is Large Family.
대 of 대문(大門) is also a Chinese character.
대(大) means Great, Big, Large, ......
문 is door.
대문 is gate, entrance of hole house.
so, 대문 is of course big than 문. because entrance gate is big than door.
well, my english is poor and so my explain is also poor.
but i just hope you understand well.
thank you.
BUT, WE USUALLY THINK OF '대문' IS JUST ENTRANCE GATE