A "Slayer" is a term used to describe fans who hate the character of Arwen, and often support alternate relationships for the character of Aragorn.
The word came about when Maka, currently the owner of Not-Arwen.net invented it. Quoted from Not-Arwen -
"The term "Slayer" orginated about two years ago, when in a fit of boredom I descieded to act on my hatred for Arwen and build the web's first ever anti-arwen site. Now of course this new and amazingly cool creation couldn't just be called; "Audrey's way cool place of Arwen hate and squid tapdancing acedemy" Because really, no one but space aliens visit sites like those. So seeing as how Arwen is an elf, I figured the title should be in elvish. So I headed on over to the ever trusty english-to-elvish dictionary and browsed through. I figuired that not only would the site have a name in elvish, but that I'd probably also want to use it as a screen name for ease of reference. So I settled on the words "Maka" for the verb "slay" and "Undomiel" for "Evenstar" so it would roughly translate as "Slayer of the Evenstar". And thus Maka Undomiel was born."