Extension file created for AutoCAD, a design and engineering application for 2D and 3D products; contains an application component written using Autodesk's ObjectARX, an object-oriented API that allows developers to customize and extend AutoCAD using C++, C#, and VB.NET program code. ObjectARX SDKs are released with each version of AutoCAD, so you need to match the SDK version with the appropriate AutoCAD version.
The ARX file extension is used used for one of the embroidery formats - Artista Cross Stitch. This format was probably developed and used in BERNINA software programs.