You see these things everywhere in both desktop and web development. Do they have a proper term or name? I thought I heard someone call it a "thumper" once, but Google doesn't seem to agree.
Not really sure how to categorize this, since it's applicable everywhere.
The term you heard was most likely Throbber - this is from early web browsers (Mosaic, Netscape) where the page load indicator was indicated by animating the browser logo.