The dumbbell row targets the muscles of the back, especially the latissimus dorsi and rhomboids. The bicep muscles of the upper arm are also activated during the row -- just how much depends on the grip you choose to use. If your goal is to build big biceps, do not rely on the row as your only bicep exercise, though.
The dumbbell row is done by bending forward from the hips and placing a knee and hand on a workout bench. Hold a dumbbell in your unsupported hand and bend your elbow to pull it up alongside your rib cage. Extend your elbow until your arm is fully extended toward the floor to finish one repetition. Your torso should stay level to the floor throughout the movement.
The latissimus dorsi, the broad muscle along the back of the ribs, and the smaller upper back muscle of the rhomboids are the primary activators during the row. Synergist muscles are those that assist the primary muscles during execution of an exercise. The ones used during the row are the trapezius of the upper back, the posterior deltoids at the back of the shoulders, the erector spinae that lie along the spine and the rotator cuff and forearm muscles. The biceps are considered a dynamic stabilizer when it comes to the dumbbell row, meaning they help with joint stabilization as you pull the weight up and down.
The classic way of holding the dumbbell during the row is with an overhand grip. As you row, you hold the palm facing your body and the weight bench. If you change to an underhand grip and have the weight facing forward in the same direction as your head, the biceps become more active during the row.
Although the biceps assist and stabilize during a row, you should still train them independently to build strength in the upper arm. Dumbbell or barbell curls effectively target the two-headed muscle for everyday activities such as carrying groceries or lifting heavy objects. If your goal is to build significant mass in your biceps, multiple variations of the bicep curl should be a regular part of your training routine.