The key point is that the trim wheel controls the difference between the wing AoA and the tailplane AoA, with hands off the controls.
(obviously the whole aeroplane can still pitch up or down). As Genghis described, there are various ways to achieve this.
For any given AoA difference, the 'whole-aircraft AoA' is stable at a particular angle to the airflow. If you pitch down and then take your hands off, the tail rises and gets pushed down again. After a few ups and downs, you return to your original AoA. Conversely if you pitch up.
In straight-and-level flight, trimming for an AoA is effectively trimming for speed, as IO540 said.
But if you trim for 100Kts S&L, then start a hands-off banked turn, the aircraft will try to maintain the previous AoA, not the previous speed.
This means the nose will drop, and you will descend, so now the aircraft is supporting the higher G weight at a faster speed but at the original AoA.
A gust can start the turn, in which case this whole procedure can occur hands-off.
If your aircraft has a separate tendency to steepen bank angles, you will get a spiral dive.
In IMC, you won't see it happening. The "seat of the pants" won't feel any turn, though you might feel heavy as though you were pitching up...