This is the Chest Supported Row using Dumbbells. I use these often in my training programs because it is a very simple way to train the lats and upper back. Other exercises like the bent row often get butchered and many do not have the trunk stability to stay in place enough to isolate the upper-back muscles.
The chest supported row makes it difficult to cheat and is easy to cue and coach. Just be cognizant of arching the low back excessively. This video is showing how to perform it on an adjustable bench.
Boston, MA / Portsmouth, NH