For a practical use of the Script label panel, see this recent question on the Adobe forum: https://forums.adobe.com/thread/978023?tstart=0
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.