From what I have personally seen, salary bands aren't necessarily related to a salary cap. As others have mentioned, if you get to 50% of that range, it makes it very hard to get a pay raise. For example, when I started I was told that my band had a salary range of $50,000 - $250,000 and it was explained that since IBM doesn't have a definitive career path system, it's possible to stay within your same salary band for years or maybe your whole career. So, let's say you're an administrative assistant. In other organizations you might be an Admin Asst I at the low end of the payscale and after a year or two you can be promoted to Admin Asst II and take on more responsibilities. There may be a path for Admin Asst III and IV and then up to Senior Admin Asst or Executive Assistant. Lots of jobs have those sorts of growth paths within the same realm - you take on more responsibility, you get a pay increase and a title change. But IBM doesn't really do that. You're either a worker, a manager, director, VP, Pres, etc. with nothing in between. So there is wiggle room for increased pay to offset the fact your title will be 'flat' for years/decades.
Some of the bands aren't necessarily capped by salary - in theory, you can make 6 figures at a low band number - but instead they cap the job responsibilities. Using the admin example, your duties might be defined as ordering supplies, organizing calendars, maintaining meeting rooms, etc. and even if you actually do more than that, your job description doesn't say those things, so "on paper" you don't do those things. So let's say that an admin in band 4 actually takes on a ton of organizational work and would be great as a project manager, that person may not be eligible to apply for a job that is listed as a band 7. They may have the skills and experience, but their band level prevents them from being considered. THAT is where the band system falls apart. I have seen lots of people in lower bands who grow their skills and want to move "up" but they're not eligible to apply and so they get frustrated and leave IBM. I'm sure this is deliberate. If you're hired in at certain band levels, it's not about pay but rather future growth. IBM would rather you leave after a few years and replace you with someone less expensive.
Also, as others have said: raises are VERY hard to get. Regardless of how much your job grows and your skills expand and your excellent reviews, it is difficult. I had a manager start the process (someone I trusted and was actually looking out for me) and since I hadn't gotten a pay increase in a few years the proposal was for a 10% increase (which is still way behind inflation, etc.) and it took about 18 months and in the end I got a 3% increase. My manager was disappointed and the worst part is that now that I was given 'something' I won't be eligible for anything more for probably another 18-24 months.