"Stage one is to cross the river, say by swimming or rowing a boat. "

As you cross, you'll get swept downstream by the current.

When you get to the other side, you plan to walk back upstream to your destination. Walking upstream is stage two. It occurs to you that you might save some time by pointing upstream while crossing the river. It will take a little longer to cross the river that way, but you won't get swept downstream so far. That means less time walking back upstream, and you hope to come out ahead overall.