Depending on where you're from, Comic Book Boards can mean either the original bristol board one draws page panels on, or the boards that go into the bags where you store purchased comics you want to preserve. We'll start with the latter.
The storage boards, sometimes called comic backer boards, help to preserve the current condition of your comic books. Since comics are normally saddle stapled, they tend to curl up if left out in a normal home environment. Backer boards, combined with some kind of storage bag made out of polypropylene (cheap poly bags) or mylar (more expensive but chemically stable), will help to prevent this from happening. They also prevent wrinkles from moving or storing comics, and even help the edges remain nick-free. Storage boards can be purchased from most comic retailers or online, and usually come in packs of 100.
The materials they use to make the boards are also a concern. You can get cheap poster board styles, or the slightly more expensive PH-neutral boards that will help your comics survive for a long period without turning brittle and brown. Since the cheap pulp they use on comics have some acidity, that's why they deteriorate. Luckily, good boards will help to stop the comics from self-destructing.
The other type of comic book boards are the heavy bristol used by the drawer and inker, also known as the tracer in all of Kevin Smith's movies. These boards are also usually PH-neutral, and I found most artists prefer the smooth finish versus the eggshell, or rough, finish. The smooth finish does help when inking, especially if one is using a rapidograph pen. The boards are stable enough for several people to work on, yet flexible enough to wrap around a drum scanner to digitize. The vast majority of folks who own original art have a page of bristol. I personally have a page of Iron Man fighting Nick Fury, signed by the artist and inker.