Speed trim system is armed 10 sec after liftoff, 5 sec following release of the trim switches, N1 above 60% autopilot not engaged, TE flaps extended, and airspeed between 100-300 kts. It is a speed stability system designed to improve flight characteristics during operations with a low gross weight, aft center of gravity, and high thrust when the autopilot is not engaged. The purpose is to return the aircraft to a trimmed speed by commanding the stabilizer in a direction opposite the speed change. Speed trim operates the stabilizer most frequently during takeoff, climb, and go-around. (high power and low airspeed causes pitch-up) Speed trim satisfies certification requirement of a 1lb increase in stick force for 6 kt of airspeed increase. In real life flying the 737 it is something that happens in the background and is a protection feature. If you're flying and trimming correctly speed trim rarely engages. If your hand flying you trim to remove control forces at your desired airspeed if you don't speed trim might do it for you. Hope this helps