The latch stile is the leading edge of a gate as you push it open. It does less structural work than the hinge stile but carries every piece of latch hardware: the latch body, the lockbox, the drop bolt receiver, the catch plate target, sometimes the manual release key.
On a single-swing gate, the latch stile is also where the leading-edge sag shows up first. After a year of opening and closing, gravity, wind, and use will pull the latch stile out of perfect plumb. A drop bolt at the bottom of the latch stile is the cure: drop the bolt into a ground sleeve and the leading edge is now physically supported.
On a double-swing gate, the latch stile of the active leaf catches against the meeting stile of the inactive leaf, which is locked down with its own drop bolt.