This is a couple of pictures I found on internet and seam to describe things well. The shifter attaches via linkage to a lever on drivers side of transmission, just under the kickdown lever attaches. When vehicle is in park, the rod (red arrow) moves towards the tailhousing.
In the tailhousing, there is a spring-loaded pawl that is pushed into a gear splined onto the output shaft with castle style cuts into it. The (red arrow) rod goes into cavity (green arrow - which has a screwdriver inserted), pushing the pawl inwards (gold arrow direction).
The park pawl has a pivot (pink arrow) to give it some strength. When engaged in park, that pawl and gear "engagement" is what keeps car from moving. When car is taken out of park, the spring pushes the pawl out of the way.
The white circle has a spring that helps the park pawl to engage until it finds a slot in gear. If you have ever put a car in park when car is still in motion, what you year is the pawl trying to fit into the hole and the spring (white circle) that is allowing it some “give”.
Now with pictures and explanation out of the say, those gears and pawls are not always machined well (burrs, etc.) and the two items can stick – especially when parking on an incline. The park rod spring only works when going into park. The gear/pawl contact (burrs from machining) is what makes it hard to get out of park. I recommend for customers with that condition is to place parking brake on first, then place into park before turning car off. When starting, place car out of park before releasing the park brake. Over time, the two items will work smoothly, but sometimes it takes a while.
Placing car into park before coming to a complete stop can make the condition worse.
Note: the governor bolts onto the “other” side of the gear. You can see 3 (of 4) attaching bolts on the gear.
BudW