From: Wikipedia - User agent

During the first browser war, many web servers were configured to only send web pages that required advanced features, including frames, to clients that were identified as some version of Mozilla.[5] Other browsers were considered to be older products such as Mosaic, Cello or Samba and would be sent a bare bones HTML document.

For this reason, most Web browsers use a User-Agent string value as follows:

Mozilla/[version] ([system and browser information]) [platform] ([platform details]) [extensions]

webaim.org has it's own version of the history which is funny to read but I don't know how much accurate it is.

... And then Google built Chrome, and Chrome used Webkit, and it was like Safari, and wanted pages built for Safari, and so pretended to be Safari. And thus Chrome used WebKit, and pretended to be Safari, and WebKit pretended to be KHTML, and KHTML pretended to be Gecko, and all browsers pretended to be Mozilla, and Chrome called itself Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US) AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.27 Safari/525.13, and the user agent string was a complete mess, and near useless, and everyone pretended to be everyone else, and confusion abounded.

One of the first browsers was called "Mosaic" (it was very important, but could do nothing more than display very basic HTML!). And "Mozilla" was the "Mosaic Killer" (it's in the name; it could do a lot more than Mosaic). So every browser, which wants to be better than Mosaic, will state so in it's user agent. Today, every browser out there is better than Mosaic, so everyone will state that they are Mosaic killers and can do more than basic display functionalities.