Unlimited Blade Works refers to the noble phantasm of the character Archer and Shirou Emiya in the Type-Moon Fate series. Since its introduction in 2004, the ability became popular among fans, spawning parodies and a copypasta based on the noble phantasm’s incantation.
Unlimited Blade Works was first introduced in the 2004 visual novel game Fate/stay night. specifically in one of the game’s story routes under the same name as the noble phantasm. The noble phantasm is a reality marble that acts as a magical factory for creating replicas of various weapons including other noble phantasms. To summon the reality marble, Archer must use an incantation to facilitate the invocation. The incantation reads:
“I am the Bone of my Sword
Steel is my Body and Fire is my Blood.
I have created over a Thousand Blades,
Unknown to Death,
Nor known to Life.
Have withstood Pain to create many Weapons
Yet those Hands will never hold Anything.
So, as I Pray–
Unlimited Blade Works ”
Shirou Emiya has an alternate version of the incantation which he uses to summon the reality marble. The incantation is as follows:
“I am the Bone of my Sword
Steel is my Body and Fire is my Blood
I have created over a Thousand Blades
Unaware of Loss,
Nor aware of Gain.
Withstood Pain to create Weapons, Waiting for one’s Arrival
I have no Regrets. This is the only Path
My whole life was Unlimited Blade Works ”
Discussions regarding Unlimited Blade Works began as early as 2006 with posts appearing on a number of sites such as reddit,  Tumblr,  4chan,  Gamefaqs,  TVTropes,  and Zetaboards.  On December 8th, 2008, Urban Dictionary user Arblast submitted an entry regarding the noble phantasm. 
On July 31st, 2013, Youtube user ExiaFr posted a video showcasing Archer using Unlimited Blade Works which was taken from the 2010 Movie adaptation of Fate/stay night (shown below, left). Within 2 years, the video gathered over 276.000 views. On May 10th, 2015, Youtube user TheSzadow posted a video comparing Archer’s Unlimited Blade Works ability between the 2006 and the 2014 anime adaptation of Fate/stay night (shown below, right). Within a year, the video gathered over 199.000 views.
Unlimited Essay Works refers to a notorious 4chan post that was submitted by a user known as “Mike”. The post shows an essay which was written in the same manner as the copypasta which resulted in the user getting a D+ and ultimately failing his semester.
The original thread was posted on 2nd August, 2006, on 4chan’s /a/ board. In the thread, the original poster delivered a promise he made in a previous topic to turn in his final exam in the form of the Unlimited Blade Works copypasta (shown below). 
The thread gained traction among users and was subsequently stickied by a mod.  The image of the essay gained popularity on a number of sites such as Funny Exams,  Dark Mirage,  and FunnyJunk.  The thread also spawned a number of edits that pokes fun at the event(shown below).