The difference in the appearance of the two sides of the aluminum foil is simply due to its thickness and the manufacturing process. Aluminum foils are prepared by passing aluminum metal (along with a very small fraction of impurities) through a series of rollers. This processing produces very thin sheets of aluminum, in fact, so thin that if this sheet passes thorough the last set of rollers, it may tear or crimp. To avoid that, two sets of aluminum foils are rolled together during the final pass. The foil side closer to the roller gets polished (and hence the shiny appearance), while the other side stays unpolished (and hence the matte finish).
Note that there is no difference between the two sides of the foil, as far as cooking or wrapping the food is concerned.
Hope this helps.