This is a 40-pin surface mount FPC (Flat Printed Circuit) connector. Nothing too fancy here, except that it can be plugged in either way - contacts up or down. This is useful for manufacturers because they only have to keep one item in stock. It is useful for consumers because they can use one connector to fit in multiple orientations.
This product fits the 1.77 TFT LCD Display 160x128 RGB - 3 Wire and thanks to its dual-sided nature you can use it upside down or all-around.