The plant is a clematis, probably the native clematis, Virgin's Bower (Clematis virginiana). This native perennial vine grows over other vegetation in thickets and woods. The white flowers are small, delicate clusters that have a lovely scent which attracts many pollinators.  The vine may be trained to grow on a fence or trellis, but requires constant monitoring or it will wander. If you wish to remove it from your beds, it is important to get as much of the root as possible or it will reappear.

Here's a link to more info about Virgin's Bower:

http://www.westernpawildflowers.com/

Happy Gardening!