Dramatic reading, by definition, is oral interpretation commonly used in reader's theater, where a reader would read a story in a dramatic voice.
On the internet, dramatic reading involves reading something usually boring or horrible in a sarcastically dramatic voice to make it appear out of context, usually text with bad grammar and spelling as the reader will read them literally. This was a large YTMND fad in 2006 and onwards.
The concept of comedically dramatic readings predates the internet, as demonstrated here by Peter Sellers's Shakespearian version of the classic Beatles pop song A Hard Day's Night, first released in 1965.
The most significant example of dramatic readings of badly written fiction before the existence of the internet is The Eye of Argon. A fantasy novel written by the then 16 year old Jim Theis and published in in OSFAN issue 10 in 1970, the story began to circulate round the entire science fiction community, eventually becoming a popular and frequent subject of dramatic readings at conventions. These readings have even been turned into a party game, with the challenge being to read the story completely seriously without laughing once. The infamy of the story's quality lives on on the internet, the story having become a popular subject of MSTing.
The Bauman E-mails: A Dramatic Reading involves Eric Bauman of Ebaumsworld.com's cease-and-desist letters to YTMND, and was read by boomaga. The childish insults in the letter plus a dramatic reading generated hilarity, and took the YTMND top spot for several weeks. Later more YTMNDs posted excerpts of of the dramatic reading with notable phrases:
FBI Cyber Terrorism Unit via Wayback Machine
Later others posted their dramatic reading of other text.
Other variations include read fanfictions from fanfiction.net:
Lucky Star: The Rise of Konata via Wayback Machine
The most famous example of dramatic readings, Full Life Consequences was first posted to YTMND by the user blind51de on the 16th of May 2006, based on a fanfiction uploaded the same day by Fanfiction.net user squirrelking. Various adaptations of the dramatic reading would be made over the next few years, with the most popular of all by far being Youtuber Djy1991's Garry's Mod animated adaptation. This video currently has over 3 million views on Youtube, and has led to a number to a number of sequels being made by Djy1991 using other chapters from the fanfic and other fanfic's in general, and has also inspired a number of users to make their own Garry's Mod style videos.