(1) To nod off or doze while sitting (idiomatic). (2) To row a boat — to propel a boat with oars. The phrase can mean either depending on context.
授業中にうっかり船を漕いでしまって、先生に注意された。
I dozed off in class without meaning to and the teacher scolded me.
湖で二時間ほど船を漕いで、静かな風景を楽しんだ。
I rowed a boat on the lake for about two hours and enjoyed the peaceful scenery.
長い会議で何度も船を漕いでいる人がいた。
There was a person who kept dozing off several times during the long meeting.
彼は小舟を自分で船を漕いで向こう岸へ渡った。
He rowed the small boat himself to cross to the other shore.