The term "partial birth abortion" is not preferred by those in the pro-choice? movement, but is far more common in public use.
The procedure consists of pulling the fetus out of the womb with forceps, delivering the fetus entirely except for the head. Scissors are used to open the skull, and the brain is suctioned out to ensure death. The fetus is then removed.
The procedure is preferable from a legal standpont to other forms of abortion as it ensures death of the fetus, while others may not. That is not to say that there have not been D&X procedure abortions performed that still resulted in a living fetus.