Seasoning is the carbonized oil that has been burned into the surface of the pan. It's what you've been trying to scrub off the pan. You don't want to remove that! Don't scrub cast iron, just wipe it with a dish cloth or other soft item to clean it.
Personally, I like that pebbled finish on the newer pans. That's caused by the pans being cast in sand molds. In the past, pans were often milled and had very smooth surfaces. I have a hard time keeping my vintage stuff seasoned as well as I would like, whereas the seasoning tends to stay on the newer pebbled surfaces much better.
To season a piece of cast iron, you apply a very thin, very light coating of some sort of food-safe grease. Some people like Crisco, some like a liquid oil, some use bacon grease, etc. The key is to get it very thin, very light or it'll be gummy after it's baked on. Then you fire it in your stove oven or in a grill outside or over a campfire at a temp of about 400 degrees for an hour or two. The grease you applied smokes and burns and hardens onto the surface of the pan. This is exactly what you want to happen. The carbonized oil creates a protective surface that, over time, becomes thick and slick so food doesn't stick. (Sorry, channeling Dr. Seuss there for a moment!
) You do not want to scrub that off! You want to baby the surface so it not only doesn't get washed away, the layers build up over time. Pans with a very thick, slick, shiny surface are highly prized.
The seasoning, to put it simply, is burned, hardened, food-safe oil. If you add a coat or two, it's easy to tell when the oil has carbonized. The smoke stops rolling out of the stove oven, the smoke detectors stop going off, and the cats stop yelling about the noise from the smoke detectors. Every layer you put on your pans protects them even more and makes their surfaces more and more non-stick.
You NEVER put cast iron in a dishwasher as it'll kill the seasoning right now. Wash it gently by hand. There is a big controversy as to the use of soap or no soap. If you do use soap, use a mild version that doesn't cut grease. Never use steel wool on it. You can use a plastic scraper, or let a pan soak for a few minutes in plain hot water to loosen any sticky food. Cast iron is usually easiest to wash when it's still warm, but be sure you run your faucet till the water is hot before putting water in a hot pan. Contrasts between water temp and pan temp can warp or crack cast iron.
The water should bead up on the surface of the pan, just like on a freshly-waxed car. If the surface feels slightly greasy, that's fine. Any leftover grease helps build up the seasoning over time, and good seasoning feels a bit greasy even when it isn't. I generally rinse my pans in very hot water and then let them air dry, but if you use a dishtowel you may want to use one that you don't care if it gets dark marks on it, because sometimes it will. Then again in my case that's often due to cooking with charcoal or on a campfire.
It sounds more complex than it is. Just remember not to scrub too much.