What does ship's rail mean in this context?
"FOB contracts relieve the seller of responsibility once the goods are shipped. Once goods have passed the ship's rail, they are considered to be delivered into the control of the buyer. When shipping to the buyer begins, the buyer then assumes all liability."

I used to thought rail refers to narrow path attached to window or some construction beside staircase to keep someone from falling, but rail in the above paragraph doesn't seem to fit in either of my prior understanding of this word.

Question

What does ship's rail mean in this context?
"FOB contracts relieve the seller of responsibility once the goods are shipped. Once goods have passed the ship's rail, they are considered to be delivered into the control of the buyer. When shipping to the buyer begins, the buyer then assumes all liability."

I used to thought rail refers to narrow path attached to window or some construction beside staircase to keep someone from falling, but rail in the above paragraph doesn't seem to fit in either of my prior understanding of this word.

Answer

The ship's rail is the railing around the outside of the deck which stops someone walking on deck from falling overboard. The writer has used this form of words to try to explain to an uninitiated reader what FOB means.

I think your understanding of a rail is correct, although I would not describe a rail as "a narrow path". The rail is a tangible, physical object likely to be made out of metal or wood. The rail will follow a path - in this context "path" is intangible and describes the route the rail takes, eg along the side of the deck.

As an aside you can either say "I thought that ..." or "I used to think that ..."