Can you tell me anything about the dark rings inside of ceramic coffee mugs?

Those dark rings in your coffee cups exactly match the ones on the lining of your stomach. Presuming you drink the same coffee.

Most materials are porous, meaning that there are voids within the material that are filled with air. The glazing on ceramic cups and dishes protects the porous ceramic material to some degree, but degrades over time. Liquids enter these pores in the ceramic material and, depending on the type and color of the liquid, stains the ceramic base. I suspect this is the case here. You have nothing to fear from the stains. If you like, you can fill the cup with a bleach solution (probably near full strength) and let it sit overnight. That should remove the stain temporarily, but it will eventually return. Again, nothing to worry about, everything wears with time. Good luck!

Stubborn stains such as coffee or tea in glass

ceramic coffee or tea pots can be removed by using 2

tablespoons of chlorine bleach to 1 quart of water.

Gray marks caused by rubbing against metal can be

removed with a non-abrasive household cleanser and a

plastic scouring pad.

Either way, they may be unsightly but perfectly safe to drink from.

I don't think your dishwasher is getting them clean. Try boiling baking soda with water. Pour the boiling liquid into the mug and let it sit overnight. It should wash clean (no ring) in the morning. In the future you may have to make sure to get all the coffee out and washed a little before using the dishwasher.

If other things on the top shelf of your washer are not getting clean, you may have something wrong with the washer arm that accesses the top rack.

BTW, that baking soda trick works on lots of things.

Good luck!

stains from the coffee, i suppose they are ok to drink from.