If you don't know what Favicon is and what is good for, just use google to find this

Favicon in e107:

The header script is looking for the favicon in this order:

1. inside theme folder 

2. inside base folder

The automatically inserted favicon should have a name:

favicon.ico

If you need to insert more favicons, you can use meta tags field in main preferences.

Change (not knowing when exactly, but it is in 2.3.3 for sure).

if you upload site-button, favicon files are generated without your control:

for all those sizes: 32,16,48,192,167,180

Then this order/priority is used:

- favicon.ico  from the theme folder

- generated files (image with name 16x16_favicon.png)

- favicon.ico from root

There is no option to set this behavior off (f.e. to use custom way from the theme.php)