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Supervised method of classification means you classified a satellite imagery based on your knowledge of the area (i.e you created a training set; this refers to your identification of features like water body, shrub, ground etc) while unsupervised means you request the system to classify the satellite imagery based on the reflectance values and all you do is sepcify the number of classes you require.
The short and answer for this is in the supervised calssification you train the computer how to group the pixels into certain classes, so you classify few pixels and the computer will folLow your pattern for the rest of the image. In the unsupervised calssification, however, the computer will set its own rules and boundaries for the classification, and it will classify the image accordingly. Hope that helps.