This format was primarily created for program AutoCAD, usually known as Auto Computer Aided Design, which is basically used for development of 2D and 3D models. By the way, this format is the most widely used format for CAD drawings. His alternative was file type commonly known as DXF, which is mainly used for 2D graphics. The best applications to open this type of files are for example: above-mentioned AutoCAD, Adobe Illustrator, IntelliCAD, etc.
First version was released in 1982 together with AutoCAD v1.0, which was targeted on MS-DOS. Newer and newer versions were developed and released along with new versions of AutoCAD.
Actual version of certain files in this format can be acquired very simply. You just need to open the file in simple reading app, for example: Notepad (which is included in Windows), or Notepad++.
Currently there is substitute for this file format, it is known as OpenDWG. It was determined to be free version of DWG file format, however this type is not very compatible with official DWG format, therefore complications may appear during transferring files from one type to another. His pro is that he can load files from version DWG 2.5 to DWG 2013, which is the latest version.
If you want to open files in this format, you can just use program Autodesk DWG TrueView.