The seated calf raise is an isolated strength exercise for the calf muscles. it can be done with a dedicated machine, or with a barbell.
The calves has two major muscles: the gastrocnemius and the soleus. A seated calf raise works on both of these muscles, but mostly on the soleus which is the inner calf muscle, underneath the gastrocnemius. To guys looking for bulk, this may seem like a negative. But in fact, since the soleus lies under the gastroc, by thickening the soleus, you will cause your gastroc to "pop out" more.
How to do
Set up for the seated calf raise by loading up the machine with the weight you want to use.
Sit on the machine with the padding on top of your thighs and the balls of your feet on the edge of the foot pad, in a way that your heels will hang in the air.
Bring your heels all the way down as far as you can stretch them, then slowly raise your heels up as high as possible, putting the emphasis on the balls of your feet.
Pause at the top for a moment, then slowly lower your heels down to the starting position, and repeat.