The discussion centers on the .oct file extension, which may indicate an Octave file. To determine its nature, users are advised to first attempt opening the file in MATLAB. If that fails, using a text editor like Notepad can help identify if it is a text-based program file or a binary file. For those on Linux, commands like hexdump and file can be utilized to analyze the file's contents and identify its type. The file command is particularly useful as it can recognize file types based on their content rather than just their extension. Additionally, many proprietary files include a "magic" number at the beginning, which helps the operating system or programs identify the file type regardless of its extension.