Although it was brief and a bit subtle, trollwarrior said: "9 patch"
Nine Patch is an image format that adds extra information into a normal image file to define which part of it should be scaled when the image is used in a size larger than its original size. The technique in using this format is also implemented in the core of the Android OS.
If you google "lwjgl ninepatch" or "slick2d ninepatch" or some variant of those queries, you will have an answer.
Also libGDX has a nice implementation, and tooling for generating them via a GUI.