I'll give this a try, but hopefully you'll get some better answers, LOL
This is a very simplified answer.
In nature, a "bog" is a wetland area. In ponding, a "bog" is usually an area that is part of but separated from the pond. It's used as a FILTRATION system -- the roots of "bog" plants take in the nutrient rich water.
Water from the pond is pumped into the bog. In comparison, if you didn't use a bog, the water would be pumped through some sort of filter. The bogs are usually about 18" deep and have the system of PVC pipe along the bottom. The PVC pipe has either slits or holes drilled in them for the water to flow out. Then, pea gravel is added followed by plants. Pond water is pumped through the PVC pipe, where it then flows UP through the pea gravel where the plants' roots have access to it. The roots do their job, and clean water goes back into the pond -- Bogs are designed where the water from the bog will gravity-flow back into the pond.
So, to answer specific questions: a bog is used as a filter; is usually 12" - 18" deep; for plants, as there isn't sufficient water depth for fish; plants go in bare root [but when planting, they say to plant with the dirt ball intact, as the plants need this until they get started growing]; you add a "clean-out" pipe to flush it as needed.
Mine is under construction, so I'm learning as I go. Those who have bogs LOVE them. Water quality is great and they claim no algae [suspended] problems. Plus, the added benefit of beautiful plants. And if the plants get out of control, it's easy to pull them from the gravel.
Addy has an EXCELLENT thread under the POND CONSTRUCTION & EQUIPMENT section. She shows several different ways to construct a bog, as well as lists of plants that are bog-friendly.
https://www.gardenpondforum.com/topic/6894-bog-building/
Keep in mind that, as with anything, there is no RIGHT or WRONG [well......] way, just DIFFERENT ways. And lately there's been some controversy regarding bogs. You just have to do your research.
I hope this helps!