One key skill that all leaders need to have to get anything done is the ability to delegate. Rather than take on all of a division's work by herself, a good leader will dole out tasks. This specialized skill is a matter of determining what needs to be done and finding the best person to do it.
A University of North Carolina study found that MBAs had excellent delegation skills. This shows that MBA programs have a positive correlation with strong delegation skills.
MBAs do not teach only "soft" skills such as people skills and leadership skills (although they do, and these are important). They also teach the hard business skills of quantitative analysis -- the ability to look at data, determine its strengths and weaknesses and derive its meaning. These skills come from the ability to apply formulas and use data analysis software, all of which come from practice in an MBA program.
MBA programs differ from other educational programs in that they are focused more on group projects, discussions and seminars and less on lecture-based teaching. This means that every MBA graduate will have had to work with other people at many points during his education, which also means that an MBA graduate will have the communication skills necessary to work on projects with all kinds of people. These skills are essential in the business world as institutions depend on teamwork to survive.
MBA graduates tend to go on to supervisory positions in many industries. This means that an MBA graduate will know people from her studies throughout her career. What's more, these people will be in key decision-making roles. These personal relationships are invaluable in higher-level business, as they can help secure contracts and generally get things done. The ability to network is a key skill that MBA graduates offer their employers.