It's called a "favicon". Here's how you make one (in Windows, but same idea for other OSs):
Method A: Download one of the many free programs that can help you create a file of the type ".ico". Michelangelo comes to mind ...
1) Using Photoshop, or Paint, or pretty much any graphics program, create a 16x16 (pixels) image using minimal colors ... maybe 16-32, max. That will be your "favicon".
2) Save the file with the name "favicon", as an ".ico"-type, if the program allows it, or as a Bitmap ".bmp" file if it doesn't.
3) If it ended up as an ".ico" file, you're almost done. If it ended up as a ".bmp" file, find it on your hard drive, and rename the file extension from ".bmp" to ".ico". (For example: favicon.bmp => favicon.ico)
4) Upload the "favicon.ico" file to the root directory of your web site.
You're done. From there on out, it's up to the browser to request that file and use it in some way. Often, when someone bookmarks your site, that will be part of the process.
Where would we be without rhetorical questions?