The DF40C-10DS-0.4V(58) is a 10-position, 0.40 mm pitch receptacle from the Hirose DF40 series, designed for board-to-board stacking. It uses two rows of center strip contacts with gold plating, surface-mounted to the PCB. The key fit parameter is the mated stacking height: this receptacle supports both 1.5mm and 2.5mm stack heights, which sets the board-to-board gap in your assembly.
Stack height and board gap
With a height above board of 1.45mm (0.057"), the DF40C-10DS-0.4V(58) mates with a matching header to achieve either a 1.5mm or 2.5mm stack height. That 1.0mm difference lets you pick the tighter or looser gap without changing the receptacle.