Usually, a web bug is a transparent image or an image in the colour of the background of the page you are viewing. It is 1*1 pixels in size.
In effect, you won't notice the site you are viewing is bugged.
The way the bug works is to give it a special name, let's call it foo. When you access the page by content supplier bar, the page you are viewing includes a link to the logger baz. Because foo has a unique name for each site displayed by bar, baz can see who accessed the site and when. This info can be used to measure the effect of advertisements, see when people look at pages, enable them to look up the region the person is from or even link it to personal information using cookies.
AT&T is currently using web bugs on the Robinson list by the FCC in the USA.