Studio lighting is what separates many professional portrait photographers from the amateurs.
That's not to say that you can't achieve wonderful shots with natural light only - of course this is possible.
However for formal or glamor portraits, the flexibility of being able to control light totally will produce some powerful shots.
A basic studio lighting kit, flexible enough for many different shots, consists of two lights, with umbrellas and/or softboxes.
If you are shooting people it is preferable to use studio strobes, which act as a jumbo sized version of your normal on-camera flash.
The alternative to this is continuous lighting - think floodlights - which can still be effective, but produce less power overall and have heat and energy usage problems.
This setup can be used in many configurations - a common setup is to use one light on one side of a subject and the other light on the opposite side at half the power of the first light.
This setup will give a shot with some shadows to emphasise features, but the shadows won't be very dark - good if you are trying to show the full face or body of the subject.
Another option is to use just one light on one side of the subject, and the second light to be either a backdrop light or a hair light.
A backdrop light is useful to make the subject stand out from the background, but should be significantly lower power than the main light in most cases.
A hair light is usually placed behind or on a boom, pointing at the back of your subjects head.
This creates a fringe of light around the edges of hair and clothing, which is a good effect in glamor type photography.