The script is meant to pick up an object labeled “Name_of_the_textframe” (and, presumably, then do something with that object). So, before running the script, the user has to “tell” it on what to work by assigning a label. (But note the last comment on the change for CS5 and newer — apparently you don't need the Script Label panel anymore, or maybe it's even removed in its entirety.)
In my own scripts I've used labels this way, to “tag” items to be processed, such as textframes to do something with; and also to store script-specific information in. I also used it the other way around: during debugging, I sometimes have the script write interesting stuff into a label, so I can see in InDesign itself what the script thought it was doing by clicking an object and checking what's in the Script Label panel.
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I used script labels when I was automating the layout of 60+ calendars each year. For that sort of complex, repetitive work it's worth going to the trouble of labelling frames in templates so that you can have a script do all the monkey-work of placing those frames in the correct positions, etc. You can see the script in action in this video, which may give you an idea of how useful they can be. For that particular workflow, script labels were pretty much essential — but I haven't really used them in many other instances.