It contains the codes and procedures to order a strike, but it is not a computer.
According to sources from within the white house, in the 1980s it contained four items:
A black book of retaliatory options
A book listing classified site locations
A manilla folder with eight or ten pages staples together giving a discription of the procedures for the Emergency Alert System
A card with authentication codes
There is a small antenna protruding near the handle of the briefcase, which some believe means that there is communications equipment inside the case as well.