How can you tell when a simple landmark has grown up into a symbol? When it just won't stay in its place.
Early on, Mary Beton is hanging out next to a river on the Oxbridge campus thinking about women and fiction:
The river reflected whatever it chose of sky and bridge and burning tree, and when the undergraduate had oared his boat through the reflections they closed again, completely, as if he had never been. (1.2)
Well, that's a nice image—even a beautiful one. But what's it doing 91 pages later, when Mary is having her epiphany about how the writer's mind has to be both sexes at once? A leaf falls, and
somehow it was like a signal falling, a signal pointing to a force in things which one had overlooked. It seemed to point to a river, which flowed past, invisibly, round the corner, down the street, and took people and eddied them along, as the stream at Oxbridge had taken the undergraduate in his boat and the dead leaves. (6.2)
Okay, so the literal river at Oxbridge seems to be related to an invisible river that moves people and things around London. And then it comes back—along with the undergraduate—just a few pages later.
After the writer's mind has "celebrate[d] its nuptials in darkness," he
must pluck the petals from a rose or watch the swans float calmly down the river. And I saw again the current which took the boat and the undergraduate and the dead leaves; and the taxi took the man and the woman, I thought, seeing them come together across the street, and the current swept them away, I thought, hearing far off the roar of London's traffic, into that tremendous stream. (6.9)
Now that little river at Oxbridge isn't only related to that invisible river we talked about above, but also to what has to happen in a writer's mind. At this point, we can be confident we're dealing with a symbol.
Okay, so we have a symbol. Great. What does it mean? Well, what do rivers do?
They flow. Bingo.
Woolf's main argument about the room of one's own and the 500 pounds a year is an argument for being able to let your thoughts flow without interruption. Mary's thoughts are flowing nicely at Oxbridge until the beadle interrupts her. A woman writer's thoughts can't flow in a drawing room, because people are always coming in and out, interrupting her. So this lazy, flowing river symbolizes the way a writer's mind needs to operate—male or female. Slow, meandering, and uninterrupted.