A stile is the vertical side of a gate or door frame. Every gate has at least two: the hinge stile (on the hinge side) and the latch stile (on the latch side). On a double-swing gate, the meeting point of the two leaves is also a stile (sometimes called the 'meeting stile' or 'shut stile').
In a steel gate, stiles are usually RHS, sized for the gate width and infill weight. A 1 m wide, 2 m tall battened pedestrian gate runs 50x25 RHS stiles. A 3 m wide single-swing slatted driveway gate steps up to 65x35 or 75x50 RHS stiles to handle the leverage.
The stile is also where most of a gate's hardware loads concentrate. Hinge plates, latch plates, drop bolts, and lockboxes all transfer load into the stile. Sizing the stile to handle those concentrated loads matters as much as sizing it for the basic bending load from the gate weight.