A Jedi chooses to move freely in the world, both as a part of society and not attached to it. A Jedi must be able to move freely in and out of situations as needed. We must be able to interact with any facet of any society and still be able to withdraw to make our observations unhindered by outside influences. This is what makes a Jedi such a good diplomat.
Due to the nature of Jedi training and philosophy, we make excellent diplomats. Keen powers of observation and reasoning, a quiet mind, and sharp focus give the Jedi the ability to tread carefully in tricky situations.
Through meditations on the Unifying Force, a Jedi can often sense the intentions of others. Though it may sometimes seem that way, there is nothing supernatural about it. The Jedi study many things, including human psychology. With this knowledge and the use of a clear mind through meditation, a Jedi can draw upon his own subconscious to interpret extremely subtle cues and make sense out of seemingly disparate information.
Through detachment, a Jedi can go into the situation unburdened by preconceived notions and prejudices. This is not to say that the Jedi are perfect in this sense, but that Jedi training allows one to see those prejudices and acknowledge them. From there, it is a small step to brushing them aside when they are not wanted.
These factors leave the Jedi free to pursue diplomatic goals in a beneficial manner, even with the most hostile of people. They also give the Jedi an excellent viewpoint to ace as mediators in all sorts of situations, be they in business, politics, or personal encounters.