The 0.136" (3.45 mm) mating pin length and 0.305" (7.75 mm) post length define the board-to-board stack height and the through-hole solder depth respectively.
The 0.100" (2.54 mm) pitch is the baseline for standard 0.025" square pin headers — your board footprint must match this spacing, and the mating receptacle (typically a BergStik or compatible IDC socket) will also be on the same pitch. The 0.095" (2.41 mm) insulation height above the board is the clearance under the header body — check for component keep-out zones on the top layer. 5 A per contact is a signal-level rating.