that tells the web server
what type of web browser
requested the file
The header often includes browser name, version number and operating system, perhaps some other information.
The web browser I used to send this writeup, for example, sent this:
User-Agent: Mozilla/4.7 [en] (X11; I; Linux 2.2.13 i686)
Maybe the header was named "Agent" so that it would be somewhat sexy - maybe it makes net surfers think they're like James Bond, always after some information.
User-Agent: Bond/007 (James Bond; 007; UK; Licence to Kill)