Specifically for toilet bowls, if you find that a stain won't shift even after using a normal toilet bowl cleaner solution and a normal toilet brush, don't try to brush harder as this will scratch the porcelain surface. Also don't try something abrasive like steel wool or the green/blue side of a kitchen sponge.
Instead, what you want to do is dissolve the stain. Others have suggested CLR and that might work. But if not, then you can obtain "acidic toilet bowl cleaner", which contains hydrochloric acid, aka muriatic acid. This will remove most anything normally staining a toilet bowl, but make sure you handle it sturdily and carefully; it can mess you up. Gloves and eye protection are highly recommended, until the bowl is brushed, the stain is gone, and the bowl is flushed. Turn on the bathroom fan or open a window for ventilation during and after cleaning.
In general, for difficult cleaning jobs, don't try to clean harder, but clean smarter. If you're putting your whole body weight into a towel or a brush, there's almost certainly an easier way. Good luck!
In places with "hard" water (lots of calcium) you tend to get a calcium plaque in the pan after several years. It will absorb any iron in the water and turn brown.
It's pretty much a rock growing on the porcelain. A brush won't move it.
FYI, be sure to read the ingredients carefully on everything you use. I use a standard-looking Lysol toilet cleaner that's based on hydrochloric acid. It does not suggest that it's particularly strong (beyond the usual marketing hype) or has this as a primary ingredient.