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It means that the application allows you to write custom AppleScripts and access the scripts easily within the application, usually by way of a menubar icon and contextual menus. A common example would be Outlook Express and Tex-Edit Plus. Both of these have menus that contain scripts, and you can add your own scripts by simply saving compiled AppleScripts in a specified folder.
To take this a step further, check out Leonard Rosenthol's terrific OSA Menu (OS 9 and back) which puts an AppleScript icon in your menu bar for every application you are in!; and Red Sweater Software's FastScripts, which is OSX's replica. With less powerful features you can use Apple's built-in Script Menu, located within your /Applications/AppleScript folder.