You have to be sure of what you're downloading (because a .bin file extension is also used for CD/DVD images and backups). Check with the "provider" (Web Page, CD/DVD instructions, etc...) of the file that it can be executed as a program.

From Wikipedia:

A binary file is a computer file that is not a text file. The term "binary file" is often used as a term meaning "non-text file". Many binary file formats contain parts that can be interpreted as text; for example, some computer document files containing formatted text, such as older Microsoft Word document files, contain the text of the document but also contain formatting information in binary form.

If your .bin file is an installer/executable, then follow these steps:

1. Open your terminal and go to ~$ cd /Downloads (where ~/Downloads is the folder where you bin file is)
2. Give it execution permissions (just in case it doesn't have it already):
   ~/Downloads$ sudo chmod +x filename.bin
3. Write: ./ followed by the name and extension of your bin file. In this example it would be: ~/Downloads$ ./filename.bin

Note:

• If filename.bin needs administrator priviledges to be executed (like an installer would), write ~/Downloads$ sudo ./filename.bin and type your password.

• ~/Downloads folder is only an example. You can place your bin file anywhere you feel comfortable (yes, even a USB Drive or a SDCard).