Here 以 acts as a *position* and 為 acts as a verb meaning 'be' but working like 'as' in English.
The sturcture: Noun + [ 以 + spacial-or-temporal modifier ] + as + Noun
淮河 + 以北 + 為 (simplified: 为) + 北方,
(literal translation) Huai River + [ to north ] + as + the North,
(proper translation) The north land along Huai River is the North,
淮河 + 以南 + 為 (simplified: 为) + 南方。
(literal translation) Huai River + [ to south ] + as + the South.
(proper translation) The south land along Huai River is the South.
As you may see, these *literal* translations can be just weird. A bit hard to explain in English, I would say.
MORE EXAMPLES:
這個 (simplified: 这个) 星球的人們 (simplified: 们),一百公分 + 以下 + 為 (simplified: 为) 矮人。
(literal translation) The people of this planet, 100 cm + [ to lower ] + as + dwarfs.
(proper translation) On this planet people under 100 cm are dwarfs.
他 2009 年以前為男兒 (simplified: 儿) 生。
(literal translation) He year 2009 + [ to previous ] + as + a male.
(proper translation) She was a male before year 2009.
COMPARISON:
Here 以 acts as a *verb* meaning 'regard' and sometimes replaceable with 視(simplified: 视).
漁 (simplified: 渔) 民以海為 (simplified: 为) 生。
(literal translation) Fishermen regard sea as life.
(proper translation) Fishermen live on the sea.
職場 (simplified: 职场) 上韓國 (simplified: 韩国) 人以日本為主要競爭 (simplified: 竞争) 對 (simplified: 对) 手。
(proper translation) The Korean regard Japan as the first rival in business world.
LASTLY BUT NOT THE LEAST:
Very good questions! :-)
Hope I helped.