The word means 'flowing' as Rory said. It is a word used also for the flow of a river. For example: "Be a man We must be swift as the coursing river" which is from this song: https://www.youtube.com/watch?v=TVcLIfSC4OE

The sentence is from a very interesting story I read yesterday. “The story of an hour” written by Kate Chopin.

Flowing through her body. She's excited and the blood is flowing fast around her body, really romantic novel stuff, hope it ended well!! ;-)