So with X Hz, the screen is literally being "redrawn/refreshed" X times a second, right?
The short answer is yes (though that's not exactly a 'technical' explanation)
How come they didn't do this earlier? I mean, why start out at 60 Hz, only to slowly transition to 120 Hz later? Is it a technological limitation, or milking the market for all it's worth?
Who is 'they'? If you mean the monitor manufacturers, they DID. Higher refresh rates were available on quality CRTs before LCD technology even took off. 120Hz was quite rare, but quality CRTs often supported up to 75 or 85 or 100Hz.
The thing you need to keep in mind (and here comes another not-so-technical explanation) is that the refresh rate is very often tied to the monitor's resolution. On older CRTs, higher refresh rates were supported, but often only at certain resolutions. In many cases, the monitor would support a certain maximum resolution, but at that resolution you could only get so high a refresh rate. Similarly, it was also sometimes the case that the highest possible refresh rate that the monitor supported was only available at lower resolutions. I don't know the exact reason for this, but I believe it was due a combination of the CRTs monitors' own internal limitations, plus limitations of the connector bandwidth.
On LCDs, the situation is different because you basically only have 1 single 'native' resolution. In general, LCD monitors look crap when run at anything other than the native resolution. So you've got a situation in which you either want to get the highest native resolution panel that a small amount of money can afford, and refresh rates above 60Hz be damned. There are exceptions of course: more expensive TN panels can of course be bought that support both 60Hz and 120Hz natively at 1080p (with the right connectors). But such things cost money, which is why 120Hz monitors cost noticeably more. Despite all the bells and whistles you see on premium monitors like Dells and Apple Cinema Displays, the panel is the most expensive part for any monitor manufacturer to buy.
There's probably a lot more to it than that, which someone with better insider knowledge of the industry can share.