Your latissimus dorsi (or lats for short) are one of the largest muscles in the back. They are the major muscle group used when pulling weight that is either in front or above you. To fully develop your lats, it is important to work it from both angles.
Exercises such as pull-ups and pull-downs will help widen your lats and give your back an overall broader look. It is an important muscle to develop the V-taper look and give the illusion of a smaller waist.
Exercises such as dumbbells rows, barbell rows, and seated cable rows will thicken your lats develop a more powerful back.
When doing any of these back exercises, it is important to think about pushing down or back with the elbows, rather than using the arms. This will ensure you are focusing on your lats and not turning it into a bicep exercise. Your arms are merely "hooks" holding the weight while your lats do the work.