This article describes three formats that use the GBR file extension, and explains how to open and convert each type.
A file with the .GBR extension is most likely a Gerber file that stores printed circuit board designs. Most PCB design programs can export data to a Gerber file.
If it is not a Gerber file, it may be a brush file used by the GIMP image editing software. This type of file contains an image that the program uses to paint repeated strokes on the canvas.
Another use for the GBR file extension could be for a Game Boy tileset file, which could be included with the standard Game Boy, as well as the Super Game Boy and Game Boy Color. I've also seen this file extension used for a Game Boy Ripped Format file for Game Boy music, so it's unclear what its purpose is.