It might be interesting to note, that during pregnancy, cervix (lower part of uterus) does not contain too much of muscle cells (around 15%), rather the tough collagen fiber and fibroblast cells keep cervix tight and strong (under the influence of progesterone).On top of that, cervical mucous plug forms, secreted by the large glands of cervical mucosa.
I'll skip the sequence of hormones that play their role during first stage of labor, just to mention that prostagladins cause a reaction and encourage production of enzymes that digest collagen fiber, and fibroblast present goes through a shortening phase, so dilation and effacement occur.
"Thinning" of cervix is usually what happens with collagen structure - digestion and disappearing of it.
Action is upward and to the side, and of course, muscle of fundus work to pull and help with opening of present muscle cells.In certain circumstances, this action can stall and even reverse (so dilation can go from 7-8 cm back to 4 cm, for instance, if Mom is feeling threatened by something or someone), due to vertical and horizontal muscles of the uterus (this is mentioned in Ina May Gaskin's "Guide To Childbirth"). Vertical muscles pull, while horizontal are relaxed, and in case of emergency and stress on Mom's part, that gets reversed, or both types of muscles pull in the same time (that makes progress stop), which usually is painful and cramping.
Here is a nice drawing of myometrial fibers of the uterus:http://www.moondragon.org/obgyn/grap...rialfibers.jpg
All of the information I mentioned, is gathered from various books & journals, and I need to note that even today, just a fraction of information on cervix,uterus, and mechanism of dilation and early stage of labor are known:
1) Ultrasound and the Uterus (Osmers & Kurjak)
2) Human Reproduction journal
3) Human Reproductive Biology (college textbook)
4) Guide To Childbirth - Ina May Gaskin